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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 76230.s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 76230.s1 | 76230bg4 | \([1, -1, 0, -289796535, 1898910371925]\) | \(2084105208962185000201/31185000\) | \(40274428613265000\) | \([2]\) | \(11796480\) | \(3.1898\) | |
| 76230.s2 | 76230bg3 | \([1, -1, 0, -19637415, 24383814021]\) | \(648474704552553481/176469171805080\) | \(227904282902218731482520\) | \([2]\) | \(11796480\) | \(3.1898\) | |
| 76230.s3 | 76230bg2 | \([1, -1, 0, -18112815, 29672041581]\) | \(508859562767519881/62240270400\) | \(80381315603498817600\) | \([2, 2]\) | \(5898240\) | \(2.8432\) | |
| 76230.s4 | 76230bg1 | \([1, -1, 0, -1037295, 544619565]\) | \(-95575628340361/43812679680\) | \(-56582672442777169920\) | \([2]\) | \(2949120\) | \(2.4966\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 76230.s have rank \(0\).
Complex multiplication
The elliptic curves in class 76230.s do not have complex multiplication.Modular form 76230.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
