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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 272832.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
272832.v1 | 272832v2 | \([0, -1, 0, -33889, 2408449]\) | \(95743377182/190269\) | \(8554055860224\) | \([2]\) | \(524288\) | \(1.3691\) | |
272832.v2 | 272832v1 | \([0, -1, 0, -1409, 63393]\) | \(-13771804/68121\) | \(-1531281604608\) | \([2]\) | \(262144\) | \(1.0225\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 272832.v have rank \(2\).
Complex multiplication
The elliptic curves in class 272832.v do not have complex multiplication.Modular form 272832.2.a.v
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.