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SageMath
E = EllipticCurve("gi1")
E.isogeny_class()
Elliptic curves in class 193600gi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
193600.bm2 | 193600gi1 | \([0, 1, 0, 44367, -83493137]\) | \(16/5\) | \(-3018173044480000000\) | \([2]\) | \(2433024\) | \(2.2251\) | \(\Gamma_0(N)\)-optimal |
193600.bm1 | 193600gi2 | \([0, 1, 0, -2617633, -1587523137]\) | \(821516/25\) | \(60363460889600000000\) | \([2]\) | \(4866048\) | \(2.5717\) |
Rank
sage: E.rank()
The elliptic curves in class 193600gi have rank \(1\).
Complex multiplication
The elliptic curves in class 193600gi do not have complex multiplication.Modular form 193600.2.a.gi
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.