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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 270802.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
270802.i1 | 270802i2 | \([1, 1, 0, -33437336, 74402815040]\) | \(6950735348004218737/462042447104\) | \(274833622829368112384\) | \([2]\) | \(30965760\) | \(2.9777\) | |
270802.i2 | 270802i1 | \([1, 1, 0, -2219416, 1009485120]\) | \(2032601155983217/434808356864\) | \(258634150828397625344\) | \([2]\) | \(15482880\) | \(2.6311\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 270802.i have rank \(0\).
Complex multiplication
The elliptic curves in class 270802.i do not have complex multiplication.Modular form 270802.2.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.