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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 30576.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
30576.c1 | 30576q1 | \([0, -1, 0, -31915, 2072386]\) | \(1909913257984/129730653\) | \(244202905516752\) | \([2]\) | \(184320\) | \(1.5093\) | \(\Gamma_0(N)\)-optimal |
30576.c2 | 30576q2 | \([0, -1, 0, 27620, 8859376]\) | \(77366117936/1172914587\) | \(-35326010430966528\) | \([2]\) | \(368640\) | \(1.8559\) |
Rank
sage: E.rank()
The elliptic curves in class 30576.c have rank \(1\).
Complex multiplication
The elliptic curves in class 30576.c do not have complex multiplication.Modular form 30576.2.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.