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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 159120bj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 159120.t4 | 159120bj1 | \([0, 0, 0, -798123, 274441178]\) | \(18829800329506921/179562500\) | \(536170752000000\) | \([2]\) | \(1327104\) | \(1.9883\) | \(\Gamma_0(N)\)-optimal |
| 159120.t3 | 159120bj2 | \([0, 0, 0, -816843, 260891642]\) | \(20186080966364041/1834472656250\) | \(5477706000000000000\) | \([2]\) | \(2654208\) | \(2.3349\) | |
| 159120.t2 | 159120bj3 | \([0, 0, 0, -1212123, -39727222]\) | \(65959341605440921/37942580187200\) | \(113295937357696204800\) | \([2]\) | \(3981312\) | \(2.5376\) | |
| 159120.t1 | 159120bj4 | \([0, 0, 0, -13866843, -19829178358]\) | \(98757259854107414041/265151195465000\) | \(791737227239362560000\) | \([2]\) | \(7962624\) | \(2.8842\) |
Rank
sage: E.rank()
The elliptic curves in class 159120bj have rank \(1\).
Complex multiplication
The elliptic curves in class 159120bj do not have complex multiplication.Modular form 159120.2.a.bj
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
