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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 1190c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1190.c2 | 1190c1 | \([1, 0, 1, -43, -392]\) | \(-8502154921/60184250\) | \(-60184250\) | \([3]\) | \(528\) | \(0.17593\) | \(\Gamma_0(N)\)-optimal |
1190.c1 | 1190c2 | \([1, 0, 1, -5568, -160362]\) | \(-19085751483878521/80001320\) | \(-80001320\) | \([]\) | \(1584\) | \(0.72524\) |
Rank
sage: E.rank()
The elliptic curves in class 1190c have rank \(0\).
Complex multiplication
The elliptic curves in class 1190c do not have complex multiplication.Modular form 1190.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.