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SageMath
E = EllipticCurve("ek1")
E.isogeny_class()
Elliptic curves in class 369600.ek
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
369600.ek1 | 369600ek1 | \([0, -1, 0, -12033, 503937]\) | \(188183524/3465\) | \(3548160000000\) | \([2]\) | \(884736\) | \(1.2027\) | \(\Gamma_0(N)\)-optimal |
369600.ek2 | 369600ek2 | \([0, -1, 0, -33, 1451937]\) | \(-2/444675\) | \(-910694400000000\) | \([2]\) | \(1769472\) | \(1.5493\) |
Rank
sage: E.rank()
The elliptic curves in class 369600.ek have rank \(2\).
Complex multiplication
The elliptic curves in class 369600.ek do not have complex multiplication.Modular form 369600.2.a.ek
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.