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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 9200bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9200.bf2 | 9200bg1 | \([0, -1, 0, -15208, 588912]\) | \(243135625/48668\) | \(77868800000000\) | \([]\) | \(17280\) | \(1.3816\) | \(\Gamma_0(N)\)-optimal |
| 9200.bf1 | 9200bg2 | \([0, -1, 0, -1165208, 484508912]\) | \(109348914285625/1472\) | \(2355200000000\) | \([]\) | \(51840\) | \(1.9309\) |
Rank
sage: E.rank()
The elliptic curves in class 9200bg have rank \(1\).
Complex multiplication
The elliptic curves in class 9200bg do not have complex multiplication.Modular form 9200.2.a.bg
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.
