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Properties

Label 381480bv
Number of curves $6$
Conductor $381480$
CM no
Rank $2$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("bv1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 381480bv have rank \(2\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1 - T\)
\(5\)\(1 + T\)
\(11\)\(1 - T\)
\(17\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(7\) \( 1 + 7 T^{2}\) 1.7.a
\(13\) \( 1 + 2 T + 13 T^{2}\) 1.13.c
\(19\) \( 1 + 4 T + 19 T^{2}\) 1.19.e
\(23\) \( 1 + 23 T^{2}\) 1.23.a
\(29\) \( 1 + 6 T + 29 T^{2}\) 1.29.g
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 381480bv do not have complex multiplication.

Modular form 381480.2.a.bv

Copy content sage:E.q_eigenform(10)
 
\(q + q^{3} - q^{5} + q^{9} + q^{11} - 2 q^{13} - q^{15} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

Copy content sage:E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

Copy content sage:E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.

Elliptic curves in class 381480bv

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
381480.bv5 381480bv1 \([0, 1, 0, -50671, 7321130]\) \(-37256083456/38671875\) \(-14935120818750000\) \([2]\) \(2359296\) \(1.7988\) \(\Gamma_0(N)\)-optimal
381480.bv4 381480bv2 \([0, 1, 0, -953796, 358094880]\) \(15529488955216/6125625\) \(37851570203040000\) \([2, 2]\) \(4718592\) \(2.1454\)  
381480.bv1 381480bv3 \([0, 1, 0, -15259296, 22937896080]\) \(15897679904620804/2475\) \(61174254873600\) \([2]\) \(9437184\) \(2.4920\)  
381480.bv3 381480bv4 \([0, 1, 0, -1098296, 242263680]\) \(5927735656804/2401490025\) \(59357318329599206400\) \([2, 2]\) \(9437184\) \(2.4920\)  
381480.bv6 381480bv5 \([0, 1, 0, 3583504, 1766657760]\) \(102949393183198/86815346805\) \(-4291607395869935708160\) \([2]\) \(18874368\) \(2.8386\)  
381480.bv2 381480bv6 \([0, 1, 0, -8092096, -8693015200]\) \(1185450336504002/26043266205\) \(1287416084497521960960\) \([2]\) \(18874368\) \(2.8386\)