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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 207368.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
207368.i1 | 207368e2 | \([0, 1, 0, -69269552, 209981665312]\) | \(1030541881826/62236321\) | \(2219878068772054402009088\) | \([2]\) | \(24330240\) | \(3.4241\) | |
207368.i2 | 207368e1 | \([0, 1, 0, -68232712, 216915221760]\) | \(1969910093092/7889\) | \(140694515703641424896\) | \([2]\) | \(12165120\) | \(3.0775\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 207368.i have rank \(0\).
Complex multiplication
The elliptic curves in class 207368.i do not have complex multiplication.Modular form 207368.2.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.