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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 82810.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 82810.d1 | 82810y1 | \([1, 0, 1, -1242647033, 16862131065756]\) | \(-7626453723007966609/921488588800\) | \(-25640966748622457877299200\) | \([]\) | \(44706816\) | \(3.8999\) | \(\Gamma_0(N)\)-optimal |
| 82810.d2 | 82810y2 | \([1, 0, 1, 167110407, 52263752145308]\) | \(18547687612920431/42417997492000000\) | \(-1180305948934093640177428000000\) | \([]\) | \(134120448\) | \(4.4492\) |
Rank
sage: E.rank()
The elliptic curves in class 82810.d have rank \(0\).
Complex multiplication
The elliptic curves in class 82810.d do not have complex multiplication.Modular form 82810.2.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 LMFDB 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 LMFDB labels.
