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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 155610k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 155610.ew2 | 155610k1 | \([1, -1, 1, -5387, 161691]\) | \(-23711636464489/1513774080\) | \(-1103541304320\) | \([2]\) | \(266240\) | \(1.0642\) | \(\Gamma_0(N)\)-optimal |
| 155610.ew1 | 155610k2 | \([1, -1, 1, -87467, 9978459]\) | \(101513598260088169/377613600\) | \(275280314400\) | \([2]\) | \(532480\) | \(1.4107\) |
Rank
sage: E.rank()
The elliptic curves in class 155610k have rank \(1\).
Complex multiplication
The elliptic curves in class 155610k do not have complex multiplication.Modular form 155610.2.a.k
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
