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SageMath
E = EllipticCurve("gh1")
E.isogeny_class()
Elliptic curves in class 414960.gh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 414960.gh1 | 414960gh1 | \([0, 1, 0, -1160, -15372]\) | \(42180533641/726180\) | \(2974433280\) | \([2]\) | \(245760\) | \(0.61496\) | \(\Gamma_0(N)\)-optimal |
| 414960.gh2 | 414960gh2 | \([0, 1, 0, -40, -42700]\) | \(-1771561/192178350\) | \(-787162521600\) | \([2]\) | \(491520\) | \(0.96153\) |
Rank
sage: E.rank()
The elliptic curves in class 414960.gh have rank \(1\).
Complex multiplication
The elliptic curves in class 414960.gh do not have complex multiplication.Modular form 414960.2.a.gh
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
