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SageMath
E = EllipticCurve("gm1")
E.isogeny_class()
Elliptic curves in class 116160gm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 116160.dl2 | 116160gm1 | \([0, -1, 0, -645, 102357]\) | \(-16384/2475\) | \(-4489844198400\) | \([2]\) | \(184320\) | \(1.1071\) | \(\Gamma_0(N)\)-optimal |
| 116160.dl1 | 116160gm2 | \([0, -1, 0, -36945, 2723217]\) | \(192143824/1815\) | \(52680838594560\) | \([2]\) | \(368640\) | \(1.4537\) |
Rank
sage: E.rank()
The elliptic curves in class 116160gm have rank \(0\).
Complex multiplication
The elliptic curves in class 116160gm do not have complex multiplication.Modular form 116160.2.a.gm
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.
