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SageMath
E = EllipticCurve("ec1")
E.isogeny_class()
Elliptic curves in class 364650.ec
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
364650.ec1 | 364650ec1 | \([1, 1, 1, -2338, -31969]\) | \(90458382169/25788048\) | \(402938250000\) | \([2]\) | \(512000\) | \(0.93347\) | \(\Gamma_0(N)\)-optimal |
364650.ec2 | 364650ec2 | \([1, 1, 1, 6162, -201969]\) | \(1656015369191/2114999172\) | \(-33046862062500\) | \([2]\) | \(1024000\) | \(1.2800\) |
Rank
sage: E.rank()
The elliptic curves in class 364650.ec have rank \(0\).
Complex multiplication
The elliptic curves in class 364650.ec do not have complex multiplication.Modular form 364650.2.a.ec
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.