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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 35280g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
35280.y2 | 35280g1 | \([0, 0, 0, -2058, 16807]\) | \(55296/25\) | \(435818955600\) | \([2]\) | \(43008\) | \(0.92856\) | \(\Gamma_0(N)\)-optimal |
35280.y1 | 35280g2 | \([0, 0, 0, -27783, 1781542]\) | \(8503056/5\) | \(1394620657920\) | \([2]\) | \(86016\) | \(1.2751\) |
Rank
sage: E.rank()
The elliptic curves in class 35280g have rank \(0\).
Complex multiplication
The elliptic curves in class 35280g do not have complex multiplication.Modular form 35280.2.a.g
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.