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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 6300c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6300.bd2 | 6300c1 | \([0, 0, 0, -2700, -30375]\) | \(442368/175\) | \(861131250000\) | \([2]\) | \(6912\) | \(0.98852\) | \(\Gamma_0(N)\)-optimal |
6300.bd1 | 6300c2 | \([0, 0, 0, -19575, 1032750]\) | \(10536048/245\) | \(19289340000000\) | \([2]\) | \(13824\) | \(1.3351\) |
Rank
sage: E.rank()
The elliptic curves in class 6300c have rank \(1\).
Complex multiplication
The elliptic curves in class 6300c do not have complex multiplication.Modular form 6300.2.a.c
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.