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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 1380.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1380.c1 | 1380c2 | \([0, 1, 0, -1381, -20425]\) | \(-1138621087744/13687875\) | \(-3504096000\) | \([]\) | \(864\) | \(0.64321\) | |
1380.c2 | 1380c1 | \([0, 1, 0, 59, -121]\) | \(87228416/83835\) | \(-21461760\) | \([3]\) | \(288\) | \(0.093906\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1380.c have rank \(1\).
Complex multiplication
The elliptic curves in class 1380.c do not have complex multiplication.Modular form 1380.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.