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SageMath
E = EllipticCurve("cw1")
E.isogeny_class()
Elliptic curves in class 90160cw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
90160.bz2 | 90160cw1 | \([0, 0, 0, -697907, -304398094]\) | \(-78013216986489/37918720000\) | \(-18272663508090880000\) | \([2]\) | \(1548288\) | \(2.4015\) | \(\Gamma_0(N)\)-optimal |
90160.bz1 | 90160cw2 | \([0, 0, 0, -12238387, -16477226766]\) | \(420676324562824569/56350000000\) | \(27154518630400000000\) | \([2]\) | \(3096576\) | \(2.7481\) |
Rank
sage: E.rank()
The elliptic curves in class 90160cw have rank \(1\).
Complex multiplication
The elliptic curves in class 90160cw do not have complex multiplication.Modular form 90160.2.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 Cremona 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 Cremona labels.