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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 40560.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
40560.r1 | 40560l4 | \([0, -1, 0, -279920, 56881200]\) | \(490757540836/2142075\) | \(10587532174003200\) | \([2]\) | \(516096\) | \(1.9278\) | |
40560.r2 | 40560l2 | \([0, -1, 0, -26420, -105600]\) | \(1650587344/950625\) | \(1174652238240000\) | \([2, 2]\) | \(258048\) | \(1.5812\) | |
40560.r3 | 40560l1 | \([0, -1, 0, -18815, -984738]\) | \(9538484224/26325\) | \(2033051950800\) | \([2]\) | \(129024\) | \(1.2346\) | \(\Gamma_0(N)\)-optimal |
40560.r4 | 40560l3 | \([0, -1, 0, 105400, -949248]\) | \(26198797244/15234375\) | \(-75298220400000000\) | \([4]\) | \(516096\) | \(1.9278\) |
Rank
sage: E.rank()
The elliptic curves in class 40560.r have rank \(0\).
Complex multiplication
The elliptic curves in class 40560.r do not have complex multiplication.Modular form 40560.2.a.r
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.