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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 38808w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 38808.o2 | 38808w1 | \([0, 0, 0, -81291, -12470794]\) | \(-1972156/1089\) | \(-32804824963857408\) | \([2]\) | \(286720\) | \(1.8726\) | \(\Gamma_0(N)\)-optimal |
| 38808.o1 | 38808w2 | \([0, 0, 0, -1439571, -664716850]\) | \(5476248398/891\) | \(53680622668130304\) | \([2]\) | \(573440\) | \(2.2192\) |
Rank
sage: E.rank()
The elliptic curves in class 38808w have rank \(1\).
Complex multiplication
The elliptic curves in class 38808w do not have complex multiplication.Modular form 38808.2.a.w
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.
