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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 9744i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9744.e2 | 9744i1 | \([0, -1, 0, 1752, -7056]\) | \(145116956375/88397568\) | \(-362076438528\) | \([2]\) | \(7680\) | \(0.90713\) | \(\Gamma_0(N)\)-optimal |
9744.e1 | 9744i2 | \([0, -1, 0, -7208, -50064]\) | \(10112728515625/5561943408\) | \(22781720199168\) | \([2]\) | \(15360\) | \(1.2537\) |
Rank
sage: E.rank()
The elliptic curves in class 9744i have rank \(0\).
Complex multiplication
The elliptic curves in class 9744i do not have complex multiplication.Modular form 9744.2.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.