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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 229320.r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 229320.r1 | 229320ds4 | \([0, 0, 0, -11014563, -14070139202]\) | \(841356017734178/1404585\) | \(246713972868679680\) | \([2]\) | \(7864320\) | \(2.5994\) | |
| 229320.r2 | 229320ds3 | \([0, 0, 0, -1806483, 645071182]\) | \(3711757787138/1124589375\) | \(197533016906883840000\) | \([2]\) | \(7864320\) | \(2.5994\) | |
| 229320.r3 | 229320ds2 | \([0, 0, 0, -695163, -215312762]\) | \(423026849956/16769025\) | \(1472731368654873600\) | \([2, 2]\) | \(3932160\) | \(2.2529\) | |
| 229320.r4 | 229320ds1 | \([0, 0, 0, 19257, -12274598]\) | \(35969456/2985255\) | \(-65544637835738880\) | \([2]\) | \(1966080\) | \(1.9063\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 229320.r have rank \(0\).
Complex multiplication
The elliptic curves in class 229320.r do not have complex multiplication.Modular form 229320.2.a.r
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.
