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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 33600.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
33600.w1 | 33600fl1 | \([0, -1, 0, -272833, -54466463]\) | \(4386781853/27216\) | \(13934592000000000\) | \([2]\) | \(307200\) | \(1.9358\) | \(\Gamma_0(N)\)-optimal |
33600.w2 | 33600fl2 | \([0, -1, 0, -112833, -117986463]\) | \(-310288733/11573604\) | \(-5925685248000000000\) | \([2]\) | \(614400\) | \(2.2824\) |
Rank
sage: E.rank()
The elliptic curves in class 33600.w have rank \(1\).
Complex multiplication
The elliptic curves in class 33600.w do not have complex multiplication.Modular form 33600.2.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.