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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 338130.z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 338130.z1 | 338130z4 | \([1, -1, 0, -1307490, 345008060]\) | \(520300455507/193072360\) | \(91728633950413569720\) | \([2]\) | \(15925248\) | \(2.5304\) | |
| 338130.z2 | 338130z2 | \([1, -1, 0, -1155765, 478536175]\) | \(261984288445803/42250\) | \(27534931836750\) | \([2]\) | \(5308416\) | \(1.9811\) | |
| 338130.z3 | 338130z1 | \([1, -1, 0, -72015, 7538425]\) | \(-63378025803/812500\) | \(-529517919937500\) | \([2]\) | \(2654208\) | \(1.6345\) | \(\Gamma_0(N)\)-optimal |
| 338130.z4 | 338130z3 | \([1, -1, 0, 253110, 38194100]\) | \(3774555693/3515200\) | \(-1670070713708030400\) | \([2]\) | \(7962624\) | \(2.1838\) |
Rank
sage: E.rank()
The elliptic curves in class 338130.z have rank \(0\).
Complex multiplication
The elliptic curves in class 338130.z do not have complex multiplication.Modular form 338130.2.a.z
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
