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SageMath
E = EllipticCurve("lr1")
E.isogeny_class()
Elliptic curves in class 381150lr
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 381150.lr4 | 381150lr1 | \([1, -1, 1, -25932380, 68051513247]\) | \(-95575628340361/43812679680\) | \(-884104256918393280000000\) | \([2]\) | \(70778880\) | \(3.3013\) | \(\Gamma_0(N)\)-optimal |
| 381150.lr3 | 381150lr2 | \([1, -1, 1, -452820380, 3708552377247]\) | \(508859562767519881/62240270400\) | \(1255958056304669025000000\) | \([2, 2]\) | \(141557760\) | \(3.6479\) | |
| 381150.lr1 | 381150lr3 | \([1, -1, 1, -7244913380, 237356551577247]\) | \(2084105208962185000201/31185000\) | \(629287947082265625000\) | \([2]\) | \(283115520\) | \(3.9945\) | |
| 381150.lr2 | 381150lr4 | \([1, -1, 1, -490935380, 3047485817247]\) | \(648474704552553481/176469171805080\) | \(3561004420347167679414375000\) | \([2]\) | \(283115520\) | \(3.9945\) |
Rank
sage: E.rank()
The elliptic curves in class 381150lr have rank \(0\).
Complex multiplication
The elliptic curves in class 381150lr do not have complex multiplication.Modular form 381150.2.a.lr
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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
