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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 4650.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4650.c1 | 4650g2 | \([1, 1, 0, -204785, -35754675]\) | \(7598212583918732621/36771465672\) | \(4596433209000\) | \([2]\) | \(37632\) | \(1.6302\) | |
4650.c2 | 4650g1 | \([1, 1, 0, -12585, -582075]\) | \(-1763710408147661/129263387328\) | \(-16157923416000\) | \([2]\) | \(18816\) | \(1.2837\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4650.c have rank \(0\).
Complex multiplication
The elliptic curves in class 4650.c do not have complex multiplication.Modular form 4650.2.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 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.