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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 44436j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
44436.l4 | 44436j1 | \([0, 1, 0, 3527, 28664]\) | \(2048000/1323\) | \(-3133623698352\) | \([2]\) | \(71280\) | \(1.0867\) | \(\Gamma_0(N)\)-optimal |
44436.l3 | 44436j2 | \([0, 1, 0, -14988, 221220]\) | \(9826000/5103\) | \(193389348241152\) | \([2]\) | \(142560\) | \(1.4333\) | |
44436.l2 | 44436j3 | \([0, 1, 0, -59953, 5798996]\) | \(-10061824000/352947\) | \(-835981166638128\) | \([2]\) | \(213840\) | \(1.6360\) | |
44436.l1 | 44436j4 | \([0, 1, 0, -967188, 365789844]\) | \(2640279346000/3087\) | \(116988618071808\) | \([2]\) | \(427680\) | \(1.9826\) |
Rank
sage: E.rank()
The elliptic curves in class 44436j have rank \(0\).
Complex multiplication
The elliptic curves in class 44436j do not have complex multiplication.Modular form 44436.2.a.j
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.