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SageMath
E = EllipticCurve("ew1")
E.isogeny_class()
Elliptic curves in class 361920.ew
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
361920.ew1 | 361920ew1 | \([0, 1, 0, -31905, 2178495]\) | \(13701674594089/31758480\) | \(8325294981120\) | \([2]\) | \(1081344\) | \(1.3599\) | \(\Gamma_0(N)\)-optimal |
361920.ew2 | 361920ew2 | \([0, 1, 0, -20385, 3784383]\) | \(-3573857582569/21617820900\) | \(-5666982042009600\) | \([2]\) | \(2162688\) | \(1.7065\) |
Rank
sage: E.rank()
The elliptic curves in class 361920.ew have rank \(2\).
Complex multiplication
The elliptic curves in class 361920.ew do not have complex multiplication.Modular form 361920.2.a.ew
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.