Show commands:
SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 70699.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 70699.a1 | 70699a3 | \([0, 1, 1, -2862689, -1865226945]\) | \(-50357871050752/19\) | \(-978887112859\) | \([]\) | \(691740\) | \(2.0889\) | |
| 70699.a2 | 70699a2 | \([0, 1, 1, -34729, -2661790]\) | \(-89915392/6859\) | \(-353378247742099\) | \([]\) | \(230580\) | \(1.5396\) | |
| 70699.a3 | 70699a1 | \([0, 1, 1, 2481, -1275]\) | \(32768/19\) | \(-978887112859\) | \([]\) | \(76860\) | \(0.99026\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 70699.a have rank \(0\).
Complex multiplication
The elliptic curves in class 70699.a do not have complex multiplication.Modular form 70699.2.a.a
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
