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SageMath
E = EllipticCurve("gv1")
E.isogeny_class()
Elliptic curves in class 414960.gv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
414960.gv1 | 414960gv1 | \([0, 1, 0, -770680, -260665900]\) | \(12359092816971484921/116188800000\) | \(475909324800000\) | \([2]\) | \(6144000\) | \(1.9792\) | \(\Gamma_0(N)\)-optimal |
414960.gv2 | 414960gv2 | \([0, 1, 0, -752760, -273346092]\) | \(-11516856136356002041/1201114687500000\) | \(-4919765760000000000\) | \([2]\) | \(12288000\) | \(2.3258\) |
Rank
sage: E.rank()
The elliptic curves in class 414960.gv have rank \(1\).
Complex multiplication
The elliptic curves in class 414960.gv do not have complex multiplication.Modular form 414960.2.a.gv
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.