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SageMath
E = EllipticCurve("ep1")
E.isogeny_class()
Elliptic curves in class 102960.ep
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 102960.ep1 | 102960eg4 | \([0, 0, 0, -511102398387, -140640367301390734]\) | \(4944928228995290413834018379264689/189679641808585500000\) | \(566380375566167365632000000\) | \([2]\) | \(464486400\) | \(5.0736\) | |
| 102960.ep2 | 102960eg3 | \([0, 0, 0, -31942398387, -2197722653390734]\) | \(-1207087636168285491836819264689/236446260657750000000000\) | \(-706024751183870976000000000000\) | \([2]\) | \(232243200\) | \(4.7270\) | |
| 102960.ep3 | 102960eg2 | \([0, 0, 0, -6360994227, -189639474165646]\) | \(9532597152396244075685450929/313550122650789880627200\) | \(936255649433296170914729164800\) | \([2]\) | \(154828800\) | \(4.5243\) | |
| 102960.ep4 | 102960eg1 | \([0, 0, 0, 127069773, -10217254696846]\) | \(75991146714893572533071/15147028085515223040000\) | \(-45228783510899087753871360000\) | \([2]\) | \(77414400\) | \(4.1777\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 102960.ep have rank \(1\).
Complex multiplication
The elliptic curves in class 102960.ep do not have complex multiplication.Modular form 102960.2.a.ep
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
