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Properties

Label 371910.ba
Number of curves $4$
Conductor $371910$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("ba1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 371910.ba have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 + T\)
\(3\)\(1 + T\)
\(5\)\(1 - T\)
\(7\)\(1\)
\(11\)\(1 + T\)
\(23\)\(1 - T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(13\) \( 1 + 2 T + 13 T^{2}\) 1.13.c
\(17\) \( 1 - 6 T + 17 T^{2}\) 1.17.ag
\(19\) \( 1 - 4 T + 19 T^{2}\) 1.19.ae
\(29\) \( 1 - 2 T + 29 T^{2}\) 1.29.ac
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 371910.ba do not have complex multiplication.

Modular form 371910.2.a.ba

Copy content sage:E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - q^{8} + q^{9} - q^{10} - q^{11} - q^{12} - 2 q^{13} - q^{15} + q^{16} + 6 q^{17} - q^{18} + 4 q^{19} + O(q^{20})\) 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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 371910.ba

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
371910.ba1 371910ba4 \([1, 1, 0, -65605755457, -6467893139918699]\) \(265436898662503851515370589836169/17149152760523437500000\) \(2017580673122821898437500000\) \([2]\) \(1132462080\) \(4.6979\)  
371910.ba2 371910ba2 \([1, 1, 0, -4108270177, -100652605477451]\) \(65179715853307296723232286089/520784732418538896000000\) \(61269802984308682575504000000\) \([2, 2]\) \(566231040\) \(4.3513\)  
371910.ba3 371910ba3 \([1, 1, 0, -1380930177, -232235305649451]\) \(-2475429904568270179255646089/196606057528071366356412000\) \(-23130506062120068180465515388000\) \([2]\) \(1132462080\) \(4.6979\)  
371910.ba4 371910ba1 \([1, 1, 0, -435136097, 892655417781]\) \(77448107425788419878921609/41892392875786371072000\) \(4928598129443390770249728000\) \([2]\) \(283115520\) \(4.0047\) \(\Gamma_0(N)\)-optimal