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SageMath
E = EllipticCurve("dw1")
E.isogeny_class()
Elliptic curves in class 306850dw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
306850.dw2 | 306850dw1 | \([1, 0, 0, 3600787, 816734417]\) | \(7023836099951/4456448000\) | \(-3275898785792000000000\) | \([]\) | \(14478912\) | \(2.8174\) | \(\Gamma_0(N)\)-optimal |
306850.dw1 | 306850dw2 | \([1, 0, 0, -59935213, 184349134417]\) | \(-32391289681150609/1228250000000\) | \(-902876614660156250000000\) | \([]\) | \(43436736\) | \(3.3667\) |
Rank
sage: E.rank()
The elliptic curves in class 306850dw have rank \(0\).
Complex multiplication
The elliptic curves in class 306850dw do not have complex multiplication.Modular form 306850.2.a.dw
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.