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SageMath
E = EllipticCurve("cw1")
E.isogeny_class()
Elliptic curves in class 25872cw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 25872.ci3 | 25872cw1 | \([0, 1, 0, -4328, 101940]\) | \(18609625/1188\) | \(572485681152\) | \([2]\) | \(34560\) | \(1.0067\) | \(\Gamma_0(N)\)-optimal |
| 25872.ci4 | 25872cw2 | \([0, 1, 0, 3512, 437492]\) | \(9938375/176418\) | \(-85014123651072\) | \([2]\) | \(69120\) | \(1.3533\) | |
| 25872.ci1 | 25872cw3 | \([0, 1, 0, -63128, -6102636]\) | \(57736239625/255552\) | \(123148030967808\) | \([2]\) | \(103680\) | \(1.5560\) | |
| 25872.ci2 | 25872cw4 | \([0, 1, 0, -31768, -12136300]\) | \(-7357983625/127552392\) | \(-61466260956807168\) | \([2]\) | \(207360\) | \(1.9026\) |
Rank
sage: E.rank()
The elliptic curves in class 25872cw have rank \(1\).
Complex multiplication
The elliptic curves in class 25872cw do not have complex multiplication.Modular form 25872.2.a.cw
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.
