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SageMath
E = EllipticCurve("dg1")
E.isogeny_class()
Elliptic curves in class 185130dg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 185130.cd1 | 185130dg1 | \([1, -1, 0, -9260334, 10848636288]\) | \(68001744211490809/1022422500\) | \(1320425909534902500\) | \([2]\) | \(7741440\) | \(2.6136\) | \(\Gamma_0(N)\)-optimal |
| 185130.cd2 | 185130dg2 | \([1, -1, 0, -8988084, 11516247738]\) | \(-62178675647294809/8362782148050\) | \(-10800265275931590810450\) | \([2]\) | \(15482880\) | \(2.9602\) |
Rank
sage: E.rank()
The elliptic curves in class 185130dg have rank \(1\).
Complex multiplication
The elliptic curves in class 185130dg do not have complex multiplication.Modular form 185130.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
