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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 2394.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2394.l1 | 2394h3 | \([1, -1, 1, -1257230, -542273507]\) | \(11165451838341046875/572244736\) | \(11263493138688\) | \([2]\) | \(27648\) | \(1.9774\) | |
| 2394.l2 | 2394h4 | \([1, -1, 1, -1255070, -544231331]\) | \(-11108001800138902875/79947274872976\) | \(-1573602211324786608\) | \([2]\) | \(55296\) | \(2.3239\) | |
| 2394.l3 | 2394h1 | \([1, -1, 1, -16910, -599011]\) | \(19804628171203875/5638671302656\) | \(152244125171712\) | \([6]\) | \(9216\) | \(1.4280\) | \(\Gamma_0(N)\)-optimal |
| 2394.l4 | 2394h2 | \([1, -1, 1, 44530, -3990499]\) | \(361682234074684125/462672528510976\) | \(-12492158269796352\) | \([6]\) | \(18432\) | \(1.7746\) |
Rank
sage: E.rank()
The elliptic curves in class 2394.l have rank \(0\).
Complex multiplication
The elliptic curves in class 2394.l do not have complex multiplication.Modular form 2394.2.a.l
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.
