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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 5220.e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5220.e1 | 5220l1 | \([0, 0, 0, -288, 837]\) | \(226492416/105125\) | \(1226178000\) | \([2]\) | \(2304\) | \(0.43849\) | \(\Gamma_0(N)\)-optimal |
| 5220.e2 | 5220l2 | \([0, 0, 0, 1017, 6318]\) | \(623331504/453125\) | \(-84564000000\) | \([2]\) | \(4608\) | \(0.78507\) |
Rank
sage: E.rank()
The elliptic curves in class 5220.e have rank \(0\).
Complex multiplication
The elliptic curves in class 5220.e do not have complex multiplication.Modular form 5220.2.a.e
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.
