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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 32370bg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
32370.bj2 | 32370bg1 | \([1, 0, 0, -286625, 137015625]\) | \(-2604150083359733274001/6605854145280000000\) | \(-6605854145280000000\) | \([7]\) | \(812224\) | \(2.2990\) | \(\Gamma_0(N)\)-optimal |
32370.bj1 | 32370bg2 | \([1, 0, 0, -39869525, -100494513555]\) | \(-7008852130127189520580731601/306494452230385793968620\) | \(-306494452230385793968620\) | \([]\) | \(5685568\) | \(3.2720\) |
Rank
sage: E.rank()
The elliptic curves in class 32370bg have rank \(0\).
Complex multiplication
The elliptic curves in class 32370bg do not have complex multiplication.Modular form 32370.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.