Properties

Label 2520.b
Number of curves $2$
Conductor $2520$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 2520.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2520.b1 2520l1 \([0, 0, 0, -243, 702]\) \(78732/35\) \(705438720\) \([2]\) \(1152\) \(0.39345\) \(\Gamma_0(N)\)-optimal
2520.b2 2520l2 \([0, 0, 0, 837, 5238]\) \(1608714/1225\) \(-49380710400\) \([2]\) \(2304\) \(0.74002\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2520.b have rank \(0\).

Complex multiplication

The elliptic curves in class 2520.b do not have complex multiplication.

Modular form 2520.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{5} - q^{7} - 4 q^{11} + 6 q^{13} + 4 q^{17} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.