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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 192556i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
192556.j2 | 192556i1 | \([0, 0, 0, -116380, 15220917]\) | \(73598976000/336973\) | \(798145561983952\) | \([2]\) | \(760320\) | \(1.7103\) | \(\Gamma_0(N)\)-optimal |
192556.j1 | 192556i2 | \([0, 0, 0, -177215, -2409066]\) | \(16241202000/9332687\) | \(353682589901758208\) | \([2]\) | \(1520640\) | \(2.0569\) |
Rank
sage: E.rank()
The elliptic curves in class 192556i have rank \(0\).
Complex multiplication
The elliptic curves in class 192556i do not have complex multiplication.Modular form 192556.2.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 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.