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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 436800.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
436800.i1 | 436800i1 | \([0, -1, 0, -19541033, -33235431063]\) | \(12893959887933721024/2850834065625\) | \(182453380200000000000\) | \([2]\) | \(28753920\) | \(2.8811\) | \(\Gamma_0(N)\)-optimal |
436800.i2 | 436800i2 | \([0, -1, 0, -17344033, -40997432063]\) | \(-1126948447816289288/766396845703125\) | \(-392395185000000000000000\) | \([2]\) | \(57507840\) | \(3.2277\) |
Rank
sage: E.rank()
The elliptic curves in class 436800.i have rank \(0\).
Complex multiplication
The elliptic curves in class 436800.i do not have complex multiplication.Modular form 436800.2.a.i
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.