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SageMath
E = EllipticCurve("gp1")
E.isogeny_class()
Elliptic curves in class 88200.gp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
88200.gp1 | 88200h2 | \([0, 0, 0, -150675, 22380750]\) | \(3721734/25\) | \(2541218400000000\) | \([2]\) | \(552960\) | \(1.7907\) | |
88200.gp2 | 88200h1 | \([0, 0, 0, -3675, 771750]\) | \(-108/5\) | \(-254121840000000\) | \([2]\) | \(276480\) | \(1.4441\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 88200.gp have rank \(0\).
Complex multiplication
The elliptic curves in class 88200.gp do not have complex multiplication.Modular form 88200.2.a.gp
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.