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SageMath
E = EllipticCurve("dg1")
E.isogeny_class()
Elliptic curves in class 15680dg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 15680.dv1 | 15680dg1 | \([0, 0, 0, -412972, -102148144]\) | \(-5154200289/20\) | \(-30224159866880\) | \([]\) | \(161280\) | \(1.7999\) | \(\Gamma_0(N)\)-optimal |
| 15680.dv2 | 15680dg2 | \([0, 0, 0, 2879828, 969197264]\) | \(1747829720511/1280000000\) | \(-1934346231480320000000\) | \([]\) | \(1128960\) | \(2.7728\) |
Rank
sage: E.rank()
The elliptic curves in class 15680dg have rank \(1\).
Complex multiplication
The elliptic curves in class 15680dg do not have complex multiplication.Modular form 15680.2.a.dg
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
