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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 439569.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
439569.w1 | 439569w1 | \([1, -1, 1, -35015, -1757154]\) | \(274625/81\) | \(1400294635921233\) | \([2]\) | \(1769472\) | \(1.6120\) | \(\Gamma_0(N)\)-optimal |
439569.w2 | 439569w2 | \([1, -1, 1, 94270, -11789670]\) | \(5359375/6561\) | \(-113423865509619873\) | \([2]\) | \(3538944\) | \(1.9586\) |
Rank
sage: E.rank()
The elliptic curves in class 439569.w have rank \(0\).
Complex multiplication
The elliptic curves in class 439569.w do not have complex multiplication.Modular form 439569.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.