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SageMath
E = EllipticCurve("ca1")
E.isogeny_class()
Elliptic curves in class 18480.ca
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 18480.ca1 | 18480t3 | \([0, 1, 0, -16294696, 22417652180]\) | \(233632133015204766393938/29145526885986328125\) | \(59690039062500000000000\) | \([2]\) | \(1966080\) | \(3.0999\) | |
| 18480.ca2 | 18480t2 | \([0, 1, 0, -4070176, -2799087676]\) | \(7282213870869695463556/912102595400390625\) | \(933993057690000000000\) | \([2, 2]\) | \(983040\) | \(2.7534\) | |
| 18480.ca3 | 18480t1 | \([0, 1, 0, -3938956, -3010246900]\) | \(26401417552259125806544/507547744790625\) | \(129932222666400000\) | \([2]\) | \(491520\) | \(2.4068\) | \(\Gamma_0(N)\)-optimal |
| 18480.ca4 | 18480t4 | \([0, 1, 0, 6054824, -14499537676]\) | \(11986661998777424518222/51295853620928503125\) | \(-105053908215661574400000\) | \([2]\) | \(1966080\) | \(3.0999\) |
Rank
sage: E.rank()
The elliptic curves in class 18480.ca have rank \(1\).
Complex multiplication
The elliptic curves in class 18480.ca do not have complex multiplication.Modular form 18480.2.a.ca
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.
