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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 7920.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7920.k1 | 7920v1 | \([0, 0, 0, -243, -1358]\) | \(14348907/1100\) | \(121651200\) | \([2]\) | \(1536\) | \(0.29608\) | \(\Gamma_0(N)\)-optimal |
7920.k2 | 7920v2 | \([0, 0, 0, 237, -6062]\) | \(13312053/151250\) | \(-16727040000\) | \([2]\) | \(3072\) | \(0.64265\) |
Rank
sage: E.rank()
The elliptic curves in class 7920.k have rank \(1\).
Complex multiplication
The elliptic curves in class 7920.k 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 LMFDB 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 LMFDB labels.