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SageMath
E = EllipticCurve("gs1")
E.isogeny_class()
Elliptic curves in class 77616gs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 77616.bq2 | 77616gs1 | \([0, 0, 0, 24549, -5617654]\) | \(4657463/41503\) | \(-14579922206158848\) | \([2]\) | \(442368\) | \(1.7828\) | \(\Gamma_0(N)\)-optimal |
| 77616.bq1 | 77616gs2 | \([0, 0, 0, -363531, -77878150]\) | \(15124197817/1294139\) | \(454628483337498624\) | \([2]\) | \(884736\) | \(2.1294\) |
Rank
sage: E.rank()
The elliptic curves in class 77616gs have rank \(1\).
Complex multiplication
The elliptic curves in class 77616gs do not have complex multiplication.Modular form 77616.2.a.gs
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.
