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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 257400.s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 257400.s1 | 257400s2 | \([0, 0, 0, -118875, 15295750]\) | \(15927506500/552123\) | \(6439962672000000\) | \([2]\) | \(1769472\) | \(1.8049\) | |
| 257400.s2 | 257400s1 | \([0, 0, 0, 2625, 837250]\) | \(686000/104247\) | \(-303984252000000\) | \([2]\) | \(884736\) | \(1.4583\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 257400.s have rank \(1\).
Complex multiplication
The elliptic curves in class 257400.s do not have complex multiplication.Modular form 257400.2.a.s
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.
