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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 344760r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 344760.r4 | 344760r1 | \([0, -1, 0, -57516, 7793460]\) | \(-17029316176/11275335\) | \(-13932515444739840\) | \([2]\) | \(2654208\) | \(1.7986\) | \(\Gamma_0(N)\)-optimal |
| 344760.r3 | 344760r2 | \([0, -1, 0, -1034336, 405163836]\) | \(24759905519524/5267025\) | \(26033073841382400\) | \([2, 2]\) | \(5308416\) | \(2.1452\) | |
| 344760.r1 | 344760r3 | \([0, -1, 0, -16548536, 25916714316]\) | \(50700519510140162/2295\) | \(22686774589440\) | \([2]\) | \(10616832\) | \(2.4918\) | |
| 344760.r2 | 344760r4 | \([0, -1, 0, -1149256, 309688300]\) | \(16981825082402/5646560625\) | \(55817973030493440000\) | \([2]\) | \(10616832\) | \(2.4918\) |
Rank
sage: E.rank()
The elliptic curves in class 344760r have rank \(0\).
Complex multiplication
The elliptic curves in class 344760r do not have complex multiplication.Modular form 344760.2.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 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.
