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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 6468e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6468.a2 | 6468e1 | \([0, -1, 0, 278, -2519]\) | \(1257728/2079\) | \(-3913476336\) | \([]\) | \(3456\) | \(0.52571\) | \(\Gamma_0(N)\)-optimal |
| 6468.a1 | 6468e2 | \([0, -1, 0, -2662, 94501]\) | \(-1108671232/1369599\) | \(-2578111244016\) | \([]\) | \(10368\) | \(1.0750\) |
Rank
sage: E.rank()
The elliptic curves in class 6468e have rank \(1\).
Complex multiplication
The elliptic curves in class 6468e do not have complex multiplication.Modular form 6468.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
