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SageMath
E = EllipticCurve("cw1")
E.isogeny_class()
Elliptic curves in class 379050.cw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
379050.cw1 | 379050cw2 | \([1, 0, 1, -1060151, 420056858]\) | \(-14600882119157955625/14450688\) | \(-130417459200\) | \([]\) | \(3265920\) | \(1.8577\) | |
379050.cw2 | 379050cw1 | \([1, 0, 1, -12776, 604118]\) | \(-25551261405625/2744515872\) | \(-24769255744800\) | \([]\) | \(1088640\) | \(1.3084\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 379050.cw have rank \(1\).
Complex multiplication
The elliptic curves in class 379050.cw do not have complex multiplication.Modular form 379050.2.a.cw
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.