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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 3696r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3696.j2 | 3696r1 | \([0, -1, 0, -26808, -323744400]\) | \(-520203426765625/11054534935707648\) | \(-45279375096658526208\) | \([2]\) | \(99840\) | \(2.4505\) | \(\Gamma_0(N)\)-optimal |
| 3696.j1 | 3696r2 | \([0, -1, 0, -7235768, -7382758032]\) | \(10228636028672744397625/167006381634183168\) | \(684058139173614256128\) | \([2]\) | \(199680\) | \(2.7971\) |
Rank
sage: E.rank()
The elliptic curves in class 3696r have rank \(0\).
Complex multiplication
The elliptic curves in class 3696r do not have complex multiplication.Modular form 3696.2.a.r
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.
