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SageMath
E = EllipticCurve("ey1")
E.isogeny_class()
Elliptic curves in class 257600.ey
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 257600.ey1 | 257600ey2 | \([0, -1, 0, -2929633, -1880692863]\) | \(1357792998752738/38897700625\) | \(79662490880000000000\) | \([2]\) | \(9437184\) | \(2.5969\) | |
| 257600.ey2 | 257600ey1 | \([0, -1, 0, -429633, 66807137]\) | \(8564808605476/3081640625\) | \(3155600000000000000\) | \([2]\) | \(4718592\) | \(2.2504\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 257600.ey have rank \(1\).
Complex multiplication
The elliptic curves in class 257600.ey do not have complex multiplication.Modular form 257600.2.a.ey
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
