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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 32368.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
32368.w1 | 32368y1 | \([0, 1, 0, -9382192, -11066758316]\) | \(-11060825617/2744\) | \(-22658610228560101376\) | \([]\) | \(1233792\) | \(2.7015\) | \(\Gamma_0(N)\)-optimal |
32368.w2 | 32368y2 | \([0, 1, 0, 3981168, -39156541036]\) | \(845095823/80707214\) | \(-666440708694966841696256\) | \([]\) | \(3701376\) | \(3.2508\) |
Rank
sage: E.rank()
The elliptic curves in class 32368.w have rank \(1\).
Complex multiplication
The elliptic curves in class 32368.w do not have complex multiplication.Modular form 32368.2.a.w
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.