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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 124950.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
124950.w1 | 124950bs2 | \([1, 1, 0, -8884950, -10197373500]\) | \(337575153545189/2448\) | \(562509281250000\) | \([2]\) | \(3686400\) | \(2.4266\) | |
124950.w2 | 124950bs1 | \([1, 1, 0, -554950, -159723500]\) | \(-82256120549/221952\) | \(-51000841500000000\) | \([2]\) | \(1843200\) | \(2.0800\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 124950.w have rank \(1\).
Complex multiplication
The elliptic curves in class 124950.w do not have complex multiplication.Modular form 124950.2.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.