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SageMath
E = EllipticCurve("cn1")
E.isogeny_class()
Elliptic curves in class 54150.cn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
54150.cn1 | 54150cm2 | \([1, 0, 0, -288403088, 1887201522042]\) | \(-27692833539889/35156250\) | \(-3367895283215881347656250\) | \([]\) | \(17729280\) | \(3.6147\) | |
54150.cn2 | 54150cm1 | \([1, 0, 0, 4819162, 12045233292]\) | \(129205871/729000\) | \(-69836676592764515625000\) | \([]\) | \(5909760\) | \(3.0654\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 54150.cn have rank \(0\).
Complex multiplication
The elliptic curves in class 54150.cn do not have complex multiplication.Modular form 54150.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.