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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 50025.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
50025.k1 | 50025e2 | \([0, -1, 1, -59476533, -176261481907]\) | \(1489157481162281146384384/2616603057861328125\) | \(40884422779083251953125\) | \([]\) | \(4665600\) | \(3.2320\) | |
50025.k2 | 50025e1 | \([0, -1, 1, -3100533, 1873464968]\) | \(210966209738334797824/25153051046653125\) | \(393016422603955078125\) | \([]\) | \(1555200\) | \(2.6827\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 50025.k have rank \(1\).
Complex multiplication
The elliptic curves in class 50025.k do not have complex multiplication.Modular form 50025.2.a.k
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.