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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 28322d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 28322.g2 | 28322d1 | \([1, -1, 0, 25667, -796335]\) | \(658503/476\) | \(-1351726167113756\) | \([2]\) | \(110592\) | \(1.5917\) | \(\Gamma_0(N)\)-optimal |
| 28322.g1 | 28322d2 | \([1, -1, 0, -115943, -6658989]\) | \(60698457/28322\) | \(80427706943268482\) | \([2]\) | \(221184\) | \(1.9383\) |
Rank
sage: E.rank()
The elliptic curves in class 28322d have rank \(0\).
Complex multiplication
The elliptic curves in class 28322d do not have complex multiplication.Modular form 28322.2.a.d
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.
