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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 2016g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2016.l3 | 2016g1 | \([0, 0, 0, -129, -520]\) | \(5088448/441\) | \(20575296\) | \([2, 2]\) | \(512\) | \(0.14410\) | \(\Gamma_0(N)\)-optimal |
2016.l1 | 2016g2 | \([0, 0, 0, -2019, -34918]\) | \(2438569736/21\) | \(7838208\) | \([2]\) | \(1024\) | \(0.49067\) | |
2016.l2 | 2016g3 | \([0, 0, 0, -444, 3008]\) | \(3241792/567\) | \(1693052928\) | \([2]\) | \(1024\) | \(0.49067\) | |
2016.l4 | 2016g4 | \([0, 0, 0, 141, -2410]\) | \(830584/7203\) | \(-2688505344\) | \([2]\) | \(1024\) | \(0.49067\) |
Rank
sage: E.rank()
The elliptic curves in class 2016g have rank \(1\).
Complex multiplication
The elliptic curves in class 2016g do not have complex multiplication.Modular form 2016.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.