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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 6300.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6300.g1 | 6300s1 | \([0, 0, 0, -18000, 928125]\) | \(28311552/49\) | \(1116281250000\) | \([2]\) | \(11520\) | \(1.2057\) | \(\Gamma_0(N)\)-optimal |
6300.g2 | 6300s2 | \([0, 0, 0, -12375, 1518750]\) | \(-574992/2401\) | \(-875164500000000\) | \([2]\) | \(23040\) | \(1.5523\) |
Rank
sage: E.rank()
The elliptic curves in class 6300.g have rank \(0\).
Complex multiplication
The elliptic curves in class 6300.g do not have complex multiplication.Modular form 6300.2.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 LMFDB 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 LMFDB labels.