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SageMath
E = EllipticCurve("hg1")
E.isogeny_class()
Elliptic curves in class 388080hg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 388080.hg1 | 388080hg1 | \([0, 0, 0, -84040488, -296538415012]\) | \(-1647408715474378752/3025\) | \(-120535071148800\) | \([]\) | \(17998848\) | \(2.8484\) | \(\Gamma_0(N)\)-optimal |
| 388080.hg2 | 388080hg2 | \([0, 0, 0, -83793528, -298367823348]\) | \(-2239956387422208/27680640625\) | \(-804066030629190252000000\) | \([]\) | \(53996544\) | \(3.3977\) |
Rank
sage: E.rank()
The elliptic curves in class 388080hg have rank \(1\).
Complex multiplication
The elliptic curves in class 388080hg do not have complex multiplication.Modular form 388080.2.a.hg
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
