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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 56784.s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 56784.s1 | 56784a2 | \([0, -1, 0, -450948, 69941520]\) | \(8207369602000/3046751253\) | \(3764758110397869312\) | \([2]\) | \(602112\) | \(2.2643\) | |
| 56784.s2 | 56784a1 | \([0, -1, 0, 87317, 7718086]\) | \(953312000000/887416803\) | \(-68534262583546032\) | \([2]\) | \(301056\) | \(1.9177\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 56784.s have rank \(1\).
Complex multiplication
The elliptic curves in class 56784.s do not have complex multiplication.Modular form 56784.2.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.
