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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 62790r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 62790.p3 | 62790r1 | \([1, 0, 1, -10998, 442936]\) | \(147098448541338841/20158603920\) | \(20158603920\) | \([2]\) | \(135168\) | \(0.99511\) | \(\Gamma_0(N)\)-optimal |
| 62790.p2 | 62790r2 | \([1, 0, 1, -11978, 359048]\) | \(190031027640231961/53970033744900\) | \(53970033744900\) | \([2, 2]\) | \(270336\) | \(1.3417\) | |
| 62790.p4 | 62790r3 | \([1, 0, 1, 31492, 2376056]\) | \(3454174425137010119/4432476805233750\) | \(-4432476805233750\) | \([2]\) | \(540672\) | \(1.6883\) | |
| 62790.p1 | 62790r4 | \([1, 0, 1, -71128, -7022872]\) | \(39795753002702893561/1759345543822230\) | \(1759345543822230\) | \([2]\) | \(540672\) | \(1.6883\) |
Rank
sage: E.rank()
The elliptic curves in class 62790r have rank \(1\).
Complex multiplication
The elliptic curves in class 62790r do not have complex multiplication.Modular form 62790.2.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.
