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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 13650.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 13650.f1 | 13650c3 | \([1, 1, 0, -640728900, 6242220642000]\) | \(1861772567578966373029167169/9401133413380800000\) | \(146892709584075000000000\) | \([2]\) | \(4423680\) | \(3.6434\) | |
| 13650.f2 | 13650c2 | \([1, 1, 0, -40728900, 94020642000]\) | \(478202393398338853167169/32244226560000000000\) | \(503816040000000000000000\) | \([2, 2]\) | \(2211840\) | \(3.2969\) | |
| 13650.f3 | 13650c1 | \([1, 1, 0, -7960900, -6872030000]\) | \(3571003510905229697089/762141946675200000\) | \(11908467916800000000000\) | \([2]\) | \(1105920\) | \(2.9503\) | \(\Gamma_0(N)\)-optimal |
| 13650.f4 | 13650c4 | \([1, 1, 0, 34983100, 403607010000]\) | \(303025056761573589385151/4678857421875000000000\) | \(-73107147216796875000000000\) | \([2]\) | \(4423680\) | \(3.6434\) |
Rank
sage: E.rank()
The elliptic curves in class 13650.f have rank \(0\).
Complex multiplication
The elliptic curves in class 13650.f do not have complex multiplication.Modular form 13650.2.a.f
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
