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SageMath
E = EllipticCurve("il1")
E.isogeny_class()
Elliptic curves in class 193600il
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
193600.gl2 | 193600il1 | \([0, 1, 0, 367, 18863]\) | \(176/5\) | \(-154880000000\) | \([]\) | \(110592\) | \(0.82724\) | \(\Gamma_0(N)\)-optimal |
193600.gl1 | 193600il2 | \([0, 1, 0, -43633, 3494863]\) | \(-296587984/125\) | \(-3872000000000\) | \([]\) | \(331776\) | \(1.3765\) |
Rank
sage: E.rank()
The elliptic curves in class 193600il have rank \(2\).
Complex multiplication
The elliptic curves in class 193600il do not have complex multiplication.Modular form 193600.2.a.il
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.