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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 179776g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 179776.p2 | 179776g1 | \([0, -1, 0, -50880353, 177424263169]\) | \(-2507141976625/889192448\) | \(-5166434230115120917250048\) | \([]\) | \(25878528\) | \(3.4530\) | \(\Gamma_0(N)\)-optimal |
| 179776.p1 | 179776g2 | \([0, -1, 0, -4423032673, 113222828173313]\) | \(-1646982616152408625/38112512\) | \(-221443386114400858406912\) | \([]\) | \(77635584\) | \(4.0023\) |
Rank
sage: E.rank()
The elliptic curves in class 179776g have rank \(2\).
Complex multiplication
The elliptic curves in class 179776g do not have complex multiplication.Modular form 179776.2.a.g
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.
