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Properties

Label 148225.be
Number of curves $2$
Conductor $148225$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("be1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 148225.be have rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(5\)\(1\)
\(7\)\(1\)
\(11\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(2\) \( 1 + T + 2 T^{2}\) 1.2.b
\(3\) \( 1 - 2 T + 3 T^{2}\) 1.3.ac
\(13\) \( 1 - T + 13 T^{2}\) 1.13.ab
\(17\) \( 1 + 5 T + 17 T^{2}\) 1.17.f
\(19\) \( 1 + 6 T + 19 T^{2}\) 1.19.g
\(23\) \( 1 + 2 T + 23 T^{2}\) 1.23.c
\(29\) \( 1 - 9 T + 29 T^{2}\) 1.29.aj
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 148225.be do not have complex multiplication.

Modular form 148225.2.a.be

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

\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 148225.be

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
148225.be1 148225be2 \([1, 1, 1, -4449838, -3614950844]\) \(-24729001\) \(-394048562355765625\) \([]\) \(3326400\) \(2.4587\)  
148225.be2 148225be1 \([1, 1, 1, -3088, 256906]\) \(-121\) \(-26914047015625\) \([]\) \(302400\) \(1.2597\) \(\Gamma_0(N)\)-optimal