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SageMath
E = EllipticCurve("ct1")
E.isogeny_class()
Elliptic curves in class 46200.ct
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 46200.ct1 | 46200cv4 | \([0, 1, 0, -337008, -75412512]\) | \(132280446972242/4611915\) | \(147581280000000\) | \([2]\) | \(294912\) | \(1.8092\) | |
| 46200.ct2 | 46200cv3 | \([0, 1, 0, -99008, 10939488]\) | \(3354200221682/315748125\) | \(10103940000000000\) | \([2]\) | \(294912\) | \(1.8092\) | |
| 46200.ct3 | 46200cv2 | \([0, 1, 0, -22008, -1072512]\) | \(73682642884/12006225\) | \(192099600000000\) | \([2, 2]\) | \(147456\) | \(1.4626\) | |
| 46200.ct4 | 46200cv1 | \([0, 1, 0, 2492, -92512]\) | \(427694384/1188495\) | \(-4753980000000\) | \([4]\) | \(73728\) | \(1.1160\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 46200.ct have rank \(0\).
Complex multiplication
The elliptic curves in class 46200.ct do not have complex multiplication.Modular form 46200.2.a.ct
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
