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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 338.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
338.c1 | 338a2 | \([1, -1, 0, -389, -2859]\) | \(-38575685889/16384\) | \(-2768896\) | \([]\) | \(84\) | \(0.19693\) | |
338.c2 | 338a1 | \([1, -1, 0, 1, 1]\) | \(351/4\) | \(-676\) | \([]\) | \(12\) | \(-0.77603\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 338.c have rank \(1\).
Complex multiplication
The elliptic curves in class 338.c do not have complex multiplication.Modular form 338.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.