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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 57330.v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 57330.v1 | 57330bi4 | \([1, -1, 0, -11302457805, 462496247840101]\) | \(1861772567578966373029167169/9401133413380800000\) | \(806298745869160711876800000\) | \([2]\) | \(70778880\) | \(4.3610\) | |
| 57330.v2 | 57330bi2 | \([1, -1, 0, -718457805, 6967238240101]\) | \(478202393398338853167169/32244226560000000000\) | \(2765462236696373760000000000\) | \([2, 2]\) | \(35389440\) | \(4.0144\) | |
| 57330.v3 | 57330bi1 | \([1, -1, 0, -140430285, -508854098075]\) | \(3571003510905229697089/762141946675200000\) | \(65365958417720750899200000\) | \([2]\) | \(17694720\) | \(3.6678\) | \(\Gamma_0(N)\)-optimal |
| 57330.v4 | 57330bi3 | \([1, -1, 0, 617101875, 29901201953125]\) | \(303025056761573589385151/4678857421875000000000\) | \(-401287451786279296875000000000\) | \([2]\) | \(70778880\) | \(4.3610\) |
Rank
sage: E.rank()
The elliptic curves in class 57330.v have rank \(0\).
Complex multiplication
The elliptic curves in class 57330.v do not have complex multiplication.Modular form 57330.2.a.v
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
