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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 185.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
185.c1 | 185c1 | \([1, 0, 1, -4, -3]\) | \(4826809/185\) | \(185\) | \([2]\) | \(6\) | \(-0.79707\) | \(\Gamma_0(N)\)-optimal |
185.c2 | 185c2 | \([1, 0, 1, 1, -9]\) | \(357911/34225\) | \(-34225\) | \([2]\) | \(12\) | \(-0.45050\) |
Rank
sage: E.rank()
The elliptic curves in class 185.c have rank \(1\).
Complex multiplication
The elliptic curves in class 185.c do not have complex multiplication.Modular form 185.2.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.