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SageMath
E = EllipticCurve("cg1")
E.isogeny_class()
Elliptic curves in class 70560cg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
70560.t2 | 70560cg1 | \([0, 0, 0, 147, -1372]\) | \(1728/5\) | \(-1016487360\) | \([2]\) | \(23040\) | \(0.41174\) | \(\Gamma_0(N)\)-optimal |
70560.t1 | 70560cg2 | \([0, 0, 0, -1323, -15778]\) | \(157464/25\) | \(40659494400\) | \([2]\) | \(46080\) | \(0.75832\) |
Rank
sage: E.rank()
The elliptic curves in class 70560cg have rank \(1\).
Complex multiplication
The elliptic curves in class 70560cg do not have complex multiplication.Modular form 70560.2.a.cg
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.