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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 466752q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
466752.q4 | 466752q1 | \([0, -1, 0, -35373469, 57048634813]\) | \(4780317300004724587829248/1393942929106031774613\) | \(1427397559404576537203712\) | \([2]\) | \(59277312\) | \(3.3409\) | \(\Gamma_0(N)\)-optimal* |
466752.q2 | 466752q2 | \([0, -1, 0, -518124849, 4539008997009]\) | \(938873405985183095624413648/138168614163375007641\) | \(2263754574452736125190144\) | \([2, 2]\) | \(118554624\) | \(3.6875\) | \(\Gamma_0(N)\)-optimal* |
466752.q1 | 466752q3 | \([0, -1, 0, -8289704769, 290509835313249]\) | \(961304494694784944316951544132/20823839690665869\) | \(1364711157967478390784\) | \([2]\) | \(237109248\) | \(4.0340\) | \(\Gamma_0(N)\)-optimal* |
466752.q3 | 466752q4 | \([0, -1, 0, -470567009, 5405921839233]\) | \(-175836167856967771687798372/90870391656586224332793\) | \(-5955281987606034797873922048\) | \([2]\) | \(237109248\) | \(4.0340\) |
Rank
sage: E.rank()
The elliptic curves in class 466752q have rank \(0\).
Complex multiplication
The elliptic curves in class 466752q do not have complex multiplication.Modular form 466752.2.a.q
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.