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SageMath
E = EllipticCurve("cn1")
E.isogeny_class()
Elliptic curves in class 129960.cn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
129960.cn1 | 129960bs2 | \([0, 0, 0, -399627, -96670746]\) | \(3721734/25\) | \(47411408677017600\) | \([2]\) | \(1327104\) | \(2.0345\) | |
129960.cn2 | 129960bs1 | \([0, 0, 0, -9747, -3333474]\) | \(-108/5\) | \(-4741140867701760\) | \([2]\) | \(663552\) | \(1.6879\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 129960.cn have rank \(0\).
Complex multiplication
The elliptic curves in class 129960.cn do not have complex multiplication.Modular form 129960.2.a.cn
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.