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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 57330t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 57330.t1 | 57330t1 | \([1, -1, 0, -10845, -425979]\) | \(564174247447/8985600\) | \(2246822323200\) | \([2]\) | \(122880\) | \(1.1702\) | \(\Gamma_0(N)\)-optimal |
| 57330.t2 | 57330t2 | \([1, -1, 0, -765, -1194075]\) | \(-198155287/2464020000\) | \(-616120808940000\) | \([2]\) | \(245760\) | \(1.5168\) |
Rank
sage: E.rank()
The elliptic curves in class 57330t have rank \(1\).
Complex multiplication
The elliptic curves in class 57330t do not have complex multiplication.Modular form 57330.2.a.t
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.
