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SageMath
E = EllipticCurve("ci1")
E.isogeny_class()
Elliptic curves in class 66066.ci
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 66066.ci1 | 66066ct4 | \([1, 0, 0, -236739, -44346411]\) | \(828279937799497/193444524\) | \(342698774381964\) | \([2]\) | \(491520\) | \(1.7796\) | |
| 66066.ci2 | 66066ct2 | \([1, 0, 0, -16519, -522631]\) | \(281397674377/96589584\) | \(171114340020624\) | \([2, 2]\) | \(245760\) | \(1.4330\) | |
| 66066.ci3 | 66066ct1 | \([1, 0, 0, -6839, 211113]\) | \(19968681097/628992\) | \(1114297696512\) | \([2]\) | \(122880\) | \(1.0864\) | \(\Gamma_0(N)\)-optimal |
| 66066.ci4 | 66066ct3 | \([1, 0, 0, 48821, -3619747]\) | \(7264187703863/7406095788\) | \(-13120350460285068\) | \([2]\) | \(491520\) | \(1.7796\) |
Rank
sage: E.rank()
The elliptic curves in class 66066.ci have rank \(1\).
Complex multiplication
The elliptic curves in class 66066.ci do not have complex multiplication.Modular form 66066.2.a.ci
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 LMFDB 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 LMFDB labels.
