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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 99225.bg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
99225.bg1 | 99225bh2 | \([1, -1, 0, -2482692, -1511563159]\) | \(-15590912409/78125\) | \(-8480292725830078125\) | \([]\) | \(1995840\) | \(2.4793\) | |
99225.bg2 | 99225bh1 | \([1, -1, 0, -2067, 1121966]\) | \(-9/5\) | \(-542738734453125\) | \([]\) | \(285120\) | \(1.5064\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 99225.bg have rank \(1\).
Complex multiplication
The elliptic curves in class 99225.bg do not have complex multiplication.Modular form 99225.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.