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SageMath
E = EllipticCurve("se1")
E.isogeny_class()
Elliptic curves in class 369600se
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
369600.se1 | 369600se1 | \([0, 1, 0, -12033, -503937]\) | \(188183524/3465\) | \(3548160000000\) | \([2]\) | \(884736\) | \(1.2027\) | \(\Gamma_0(N)\)-optimal |
369600.se2 | 369600se2 | \([0, 1, 0, -33, -1451937]\) | \(-2/444675\) | \(-910694400000000\) | \([2]\) | \(1769472\) | \(1.5493\) |
Rank
sage: E.rank()
The elliptic curves in class 369600se have rank \(0\).
Complex multiplication
The elliptic curves in class 369600se do not have complex multiplication.Modular form 369600.2.a.se
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 Cremona 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 Cremona labels.