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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 463680i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 463680.i1 | 463680i1 | \([0, 0, 0, -348, 688]\) | \(10536048/5635\) | \(2492743680\) | \([2]\) | \(245760\) | \(0.49432\) | \(\Gamma_0(N)\)-optimal |
| 463680.i2 | 463680i2 | \([0, 0, 0, 1332, 5392]\) | \(147704148/92575\) | \(-163808870400\) | \([2]\) | \(491520\) | \(0.84089\) |
Rank
sage: E.rank()
The elliptic curves in class 463680i have rank \(2\).
Complex multiplication
The elliptic curves in class 463680i do not have complex multiplication.Modular form 463680.2.a.i
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 Cremona 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 Cremona labels.
