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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 2520.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2520.l1 | 2520q3 | \([0, 0, 0, -1823547, -920156186]\) | \(898353183174324196/29899176238575\) | \(22319615465391283200\) | \([2]\) | \(61440\) | \(2.4855\) | |
2520.l2 | 2520q2 | \([0, 0, 0, -280047, 37122514]\) | \(13015144447800784/4341909875625\) | \(810304588628640000\) | \([2, 2]\) | \(30720\) | \(2.1390\) | |
2520.l3 | 2520q1 | \([0, 0, 0, -251922, 48659389]\) | \(151591373397612544/32558203125\) | \(379758881250000\) | \([4]\) | \(15360\) | \(1.7924\) | \(\Gamma_0(N)\)-optimal |
2520.l4 | 2520q4 | \([0, 0, 0, 813453, 256041214]\) | \(79743193254623804/84085819746075\) | \(-62769728097166003200\) | \([2]\) | \(61440\) | \(2.4855\) |
Rank
sage: E.rank()
The elliptic curves in class 2520.l have rank \(0\).
Complex multiplication
The elliptic curves in class 2520.l do not have complex multiplication.Modular form 2520.2.a.l
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.