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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 185130.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
185130.c1 | 185130fk2 | \([1, -1, 0, -169725, 26954461]\) | \(11304275372307/635800\) | \(30411679062600\) | \([2]\) | \(1105920\) | \(1.6518\) | |
185130.c2 | 185130fk1 | \([1, -1, 0, -10005, 472885]\) | \(-2315685267/658240\) | \(-31485032441280\) | \([2]\) | \(552960\) | \(1.3053\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 185130.c have rank \(1\).
Complex multiplication
The elliptic curves in class 185130.c do not have complex multiplication.Modular form 185130.2.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.