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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 50025.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
50025.w1 | 50025u1 | \([1, 0, 1, -1001, 12023]\) | \(7088952961/50025\) | \(781640625\) | \([2]\) | \(49152\) | \(0.53908\) | \(\Gamma_0(N)\)-optimal |
50025.w2 | 50025u2 | \([1, 0, 1, -376, 27023]\) | \(-374805361/20020005\) | \(-312812578125\) | \([2]\) | \(98304\) | \(0.88565\) |
Rank
sage: E.rank()
The elliptic curves in class 50025.w have rank \(0\).
Complex multiplication
The elliptic curves in class 50025.w do not have complex multiplication.Modular form 50025.2.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.