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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 79350.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
79350.c1 | 79350m2 | \([1, 1, 0, -39080150, -17158447500]\) | \(234542659463/131220000\) | \(3692925816205857187500000\) | \([2]\) | \(16957440\) | \(3.4043\) | |
79350.c2 | 79350m1 | \([1, 1, 0, 9587850, -2120035500]\) | \(3463512697/2073600\) | \(-58357346231401200000000\) | \([2]\) | \(8478720\) | \(3.0577\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 79350.c have rank \(0\).
Complex multiplication
The elliptic curves in class 79350.c do not have complex multiplication.Modular form 79350.2.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.