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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 7920k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7920.bg1 | 7920k1 | \([0, 0, 0, -342, -2349]\) | \(379275264/15125\) | \(176418000\) | \([2]\) | \(3072\) | \(0.34888\) | \(\Gamma_0(N)\)-optimal |
7920.bg2 | 7920k2 | \([0, 0, 0, 153, -8586]\) | \(2122416/171875\) | \(-32076000000\) | \([2]\) | \(6144\) | \(0.69545\) |
Rank
sage: E.rank()
The elliptic curves in class 7920k have rank \(1\).
Complex multiplication
The elliptic curves in class 7920k do not have complex multiplication.Modular form 7920.2.a.k
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.