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SageMath
E = EllipticCurve("io1")
E.isogeny_class()
Elliptic curves in class 369600io
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 369600.io3 | 369600io1 | \([0, -1, 0, -266133, -53538363]\) | \(-130287139815424/2250652635\) | \(-36010442160000000\) | \([2]\) | \(3981312\) | \(1.9748\) | \(\Gamma_0(N)\)-optimal |
| 369600.io2 | 369600io2 | \([0, -1, 0, -4275633, -3401470863]\) | \(33766427105425744/9823275\) | \(2514758400000000\) | \([2]\) | \(7962624\) | \(2.3214\) | |
| 369600.io4 | 369600io3 | \([0, -1, 0, 1029867, -257334363]\) | \(7549996227362816/6152409907875\) | \(-98438558526000000000\) | \([2]\) | \(11943936\) | \(2.5241\) | |
| 369600.io1 | 369600io4 | \([0, -1, 0, -4959633, -2239858863]\) | \(52702650535889104/22020583921875\) | \(5637269484000000000000\) | \([2]\) | \(23887872\) | \(2.8707\) |
Rank
sage: E.rank()
The elliptic curves in class 369600io have rank \(1\).
Complex multiplication
The elliptic curves in class 369600io do not have complex multiplication.Modular form 369600.2.a.io
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
