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SageMath
E = EllipticCurve("gw1")
E.isogeny_class()
Elliptic curves in class 73920.gw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
73920.gw1 | 73920de2 | \([0, 1, 0, -2065, 35375]\) | \(59466754384/121275\) | \(1986969600\) | \([2]\) | \(61440\) | \(0.67064\) | |
73920.gw2 | 73920de1 | \([0, 1, 0, -85, 923]\) | \(-67108864/343035\) | \(-351267840\) | \([2]\) | \(30720\) | \(0.32407\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 73920.gw have rank \(1\).
Complex multiplication
The elliptic curves in class 73920.gw do not have complex multiplication.Modular form 73920.2.a.gw
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.