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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 4864.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4864.i1 | 4864m2 | \([0, 0, 0, -200, 1088]\) | \(27000000/19\) | \(622592\) | \([2]\) | \(576\) | \(0.047963\) | |
4864.i2 | 4864m1 | \([0, 0, 0, -10, 24]\) | \(-216000/361\) | \(-184832\) | \([2]\) | \(288\) | \(-0.29861\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4864.i have rank \(1\).
Complex multiplication
The elliptic curves in class 4864.i do not have complex multiplication.Modular form 4864.2.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.