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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 122010c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
122010.e1 | 122010c1 | \([1, 1, 0, -2573, -46563]\) | \(16022066761/1673280\) | \(196859718720\) | \([2]\) | \(211968\) | \(0.90216\) | \(\Gamma_0(N)\)-optimal |
122010.e2 | 122010c2 | \([1, 1, 0, 3307, -221787]\) | \(33980740919/202536600\) | \(-23828228453400\) | \([2]\) | \(423936\) | \(1.2487\) |
Rank
sage: E.rank()
The elliptic curves in class 122010c have rank \(0\).
Complex multiplication
The elliptic curves in class 122010c do not have complex multiplication.Modular form 122010.2.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.