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SageMath
E = EllipticCurve("dg1")
E.isogeny_class()
Elliptic curves in class 267696.dg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 267696.dg1 | 267696dg2 | \([0, 0, 0, -316875, 51642682]\) | \(244140625/61347\) | \(884180473880850432\) | \([2]\) | \(2752512\) | \(2.1536\) | |
| 267696.dg2 | 267696dg1 | \([0, 0, 0, 48165, 5136586]\) | \(857375/1287\) | \(-18549240710787072\) | \([2]\) | \(1376256\) | \(1.8070\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 267696.dg have rank \(1\).
Complex multiplication
The elliptic curves in class 267696.dg do not have complex multiplication.Modular form 267696.2.a.dg
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.
