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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 388416c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
388416.c1 | 388416c1 | \([0, -1, 0, -108760, -10834214]\) | \(92100460096/20253807\) | \(31288170494411712\) | \([2]\) | \(4976640\) | \(1.8787\) | \(\Gamma_0(N)\)-optimal |
388416.c2 | 388416c2 | \([0, -1, 0, 242375, -66664679]\) | \(15926924096/28588707\) | \(-2826493492565127168\) | \([2]\) | \(9953280\) | \(2.2253\) |
Rank
sage: E.rank()
The elliptic curves in class 388416c have rank \(0\).
Complex multiplication
The elliptic curves in class 388416c do not have complex multiplication.Modular form 388416.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.