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SageMath
E = EllipticCurve("cf1")
E.isogeny_class()
Elliptic curves in class 30600.cf
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
30600.cf1 | 30600ci1 | \([0, 0, 0, -975, -4750]\) | \(35152/17\) | \(49572000000\) | \([2]\) | \(24576\) | \(0.74582\) | \(\Gamma_0(N)\)-optimal |
30600.cf2 | 30600ci2 | \([0, 0, 0, 3525, -36250]\) | \(415292/289\) | \(-3370896000000\) | \([2]\) | \(49152\) | \(1.0924\) |
Rank
sage: E.rank()
The elliptic curves in class 30600.cf have rank \(0\).
Complex multiplication
The elliptic curves in class 30600.cf do not have complex multiplication.Modular form 30600.2.a.cf
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.