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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 2520.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2520.q1 | 2520d1 | \([0, 0, 0, -2862, -57591]\) | \(8232302592/214375\) | \(67512690000\) | \([2]\) | \(2304\) | \(0.85969\) | \(\Gamma_0(N)\)-optimal |
2520.q2 | 2520d2 | \([0, 0, 0, 513, -185166]\) | \(2963088/2941225\) | \(-14820385708800\) | \([2]\) | \(4608\) | \(1.2063\) |
Rank
sage: E.rank()
The elliptic curves in class 2520.q have rank \(1\).
Complex multiplication
The elliptic curves in class 2520.q do not have complex multiplication.Modular form 2520.2.a.q
sage: E.q_eigenform(10)
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.