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SageMath
E = EllipticCurve("ci1")
E.isogeny_class()
Elliptic curves in class 18480.ci
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 18480.ci1 | 18480cw3 | \([0, 1, 0, -14096, -648876]\) | \(75627935783569/396165\) | \(1622691840\) | \([2]\) | \(24576\) | \(0.96329\) | |
| 18480.ci2 | 18480cw2 | \([0, 1, 0, -896, -9996]\) | \(19443408769/1334025\) | \(5464166400\) | \([2, 2]\) | \(12288\) | \(0.61672\) | |
| 18480.ci3 | 18480cw1 | \([0, 1, 0, -176, 660]\) | \(148035889/31185\) | \(127733760\) | \([2]\) | \(6144\) | \(0.27015\) | \(\Gamma_0(N)\)-optimal |
| 18480.ci4 | 18480cw4 | \([0, 1, 0, 784, -41580]\) | \(12994449551/192163125\) | \(-787100160000\) | \([2]\) | \(24576\) | \(0.96329\) |
Rank
sage: E.rank()
The elliptic curves in class 18480.ci have rank \(1\).
Complex multiplication
The elliptic curves in class 18480.ci do not have complex multiplication.Modular form 18480.2.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.
