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SageMath
E = EllipticCurve("cq1")
E.isogeny_class()
Elliptic curves in class 47190.cq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
47190.cq1 | 47190cl2 | \([1, 0, 0, -2868841, 1877251025]\) | \(-21580315425730848803929/96405029296875000\) | \(-11665008544921875000\) | \([]\) | \(2332800\) | \(2.5108\) | |
47190.cq2 | 47190cl1 | \([1, 0, 0, 84824, 13627406]\) | \(557820238477845431/985142146218750\) | \(-119202199692468750\) | \([]\) | \(777600\) | \(1.9615\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 47190.cq have rank \(0\).
Complex multiplication
The elliptic curves in class 47190.cq do not have complex multiplication.Modular form 47190.2.a.cq
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.