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SageMath
E = EllipticCurve("cy1")
E.isogeny_class()
Elliptic curves in class 366912cy
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 366912.cy3 | 366912cy1 | \([0, 0, 0, -198156, -30419984]\) | \(38272753/4368\) | \(98206067334316032\) | \([2]\) | \(3538944\) | \(1.9928\) | \(\Gamma_0(N)\)-optimal |
| 366912.cy2 | 366912cy2 | \([0, 0, 0, -762636, 224047600]\) | \(2181825073/298116\) | \(6702564095567069184\) | \([2, 2]\) | \(7077888\) | \(2.3394\) | |
| 366912.cy1 | 366912cy3 | \([0, 0, 0, -11769996, 15541889776]\) | \(8020417344913/187278\) | \(4210585136958799872\) | \([2]\) | \(14155776\) | \(2.6860\) | |
| 366912.cy4 | 366912cy4 | \([0, 0, 0, 1213044, 1192130800]\) | \(8780064047/32388174\) | \(-728185713525536587776\) | \([2]\) | \(14155776\) | \(2.6860\) |
Rank
sage: E.rank()
The elliptic curves in class 366912cy have rank \(1\).
Complex multiplication
The elliptic curves in class 366912cy do not have complex multiplication.Modular form 366912.2.a.cy
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.
