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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 242760.o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 242760.o1 | 242760o3 | \([0, -1, 0, -1942176, 1042439580]\) | \(32779037733124/315\) | \(7785814256640\) | \([2]\) | \(2621440\) | \(2.0519\) | |
| 242760.o2 | 242760o6 | \([0, -1, 0, -1872816, -982525620]\) | \(14695548366242/57421875\) | \(2838578114400000000\) | \([2]\) | \(5242880\) | \(2.3985\) | |
| 242760.o3 | 242760o4 | \([0, -1, 0, -173496, 1040796]\) | \(23366901604/13505625\) | \(333816786253440000\) | \([2, 2]\) | \(2621440\) | \(2.0519\) | |
| 242760.o4 | 242760o2 | \([0, -1, 0, -121476, 16293060]\) | \(32082281296/99225\) | \(613132872710400\) | \([2, 2]\) | \(1310720\) | \(1.7054\) | |
| 242760.o5 | 242760o1 | \([0, -1, 0, -4431, 468576]\) | \(-24918016/229635\) | \(-88685290517040\) | \([2]\) | \(655360\) | \(1.3588\) | \(\Gamma_0(N)\)-optimal |
| 242760.o6 | 242760o5 | \([0, -1, 0, 693504, 7629996]\) | \(746185003198/432360075\) | \(-21373176101186918400\) | \([2]\) | \(5242880\) | \(2.3985\) |
Rank
sage: E.rank()
The elliptic curves in class 242760.o have rank \(1\).
Complex multiplication
The elliptic curves in class 242760.o do not have complex multiplication.Modular form 242760.2.a.o
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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
