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SageMath
E = EllipticCurve("dg1")
E.isogeny_class()
Elliptic curves in class 15680.dg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 15680.dg1 | 15680cr2 | \([0, -1, 0, -1539841, -734980959]\) | \(-5452947409/250\) | \(-18512297918464000\) | \([]\) | \(241920\) | \(2.1971\) | |
| 15680.dg2 | 15680cr1 | \([0, -1, 0, -3201, -2618335]\) | \(-49/40\) | \(-2961967666954240\) | \([]\) | \(80640\) | \(1.6478\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 15680.dg have rank \(1\).
Complex multiplication
The elliptic curves in class 15680.dg 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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
