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SageMath
E = EllipticCurve("gd1")
E.isogeny_class()
Elliptic curves in class 193600gd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
193600.s2 | 193600gd1 | \([0, 1, 0, 15327, -235457]\) | \(34295/22\) | \(-255422247731200\) | \([]\) | \(829440\) | \(1.4534\) | \(\Gamma_0(N)\)-optimal |
193600.s1 | 193600gd2 | \([0, 1, 0, -178273, 33489663]\) | \(-53969305/10648\) | \(-123624367901900800\) | \([]\) | \(2488320\) | \(2.0027\) |
Rank
sage: E.rank()
The elliptic curves in class 193600gd have rank \(2\).
Complex multiplication
The elliptic curves in class 193600gd do not have complex multiplication.Modular form 193600.2.a.gd
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.