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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 22344bj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 22344.r3 | 22344bj1 | \([0, 1, 0, -45684, -3773568]\) | \(350104249168/2793\) | \(84119976192\) | \([2]\) | \(61440\) | \(1.2684\) | \(\Gamma_0(N)\)-optimal |
| 22344.r2 | 22344bj2 | \([0, 1, 0, -46664, -3604224]\) | \(93280467172/7800849\) | \(939788374017024\) | \([2, 2]\) | \(122880\) | \(1.6150\) | |
| 22344.r4 | 22344bj3 | \([0, 1, 0, 49376, -16435168]\) | \(55251546334/517244049\) | \(-124627446007400448\) | \([2]\) | \(245760\) | \(1.9616\) | |
| 22344.r1 | 22344bj4 | \([0, 1, 0, -158384, 20080416]\) | \(1823652903746/328593657\) | \(79173048632100864\) | \([2]\) | \(245760\) | \(1.9616\) |
Rank
sage: E.rank()
The elliptic curves in class 22344bj have rank \(1\).
Complex multiplication
The elliptic curves in class 22344bj do not have complex multiplication.Modular form 22344.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
