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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 10350.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10350.w1 | 10350s2 | \([1, -1, 0, -38292, 2893616]\) | \(545138290809/16928\) | \(192820500000\) | \([2]\) | \(25600\) | \(1.2621\) | |
10350.w2 | 10350s1 | \([1, -1, 0, -2292, 49616]\) | \(-116930169/23552\) | \(-268272000000\) | \([2]\) | \(12800\) | \(0.91554\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 10350.w have rank \(1\).
Complex multiplication
The elliptic curves in class 10350.w do not have complex multiplication.Modular form 10350.2.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.