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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 5808j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5808.r2 | 5808j1 | \([0, 1, 0, -111360, -14293116]\) | \(63253004/243\) | \(586732839846912\) | \([2]\) | \(63360\) | \(1.6922\) | \(\Gamma_0(N)\)-optimal |
| 5808.r1 | 5808j2 | \([0, 1, 0, -164600, 720564]\) | \(102129622/59049\) | \(285152160165599232\) | \([2]\) | \(126720\) | \(2.0388\) |
Rank
sage: E.rank()
The elliptic curves in class 5808j have rank \(0\).
Complex multiplication
The elliptic curves in class 5808j do not have complex multiplication.Modular form 5808.2.a.j
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.
