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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 154560.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
154560.n1 | 154560dp4 | \([0, -1, 0, -2362886401, -44206810293599]\) | \(5565604209893236690185614401/229307220930246900000\) | \(60111512123538643353600000\) | \([2]\) | \(117964800\) | \(4.0279\) | |
154560.n2 | 154560dp3 | \([0, -1, 0, -720369921, 6863025539745]\) | \(157706830105239346386477121/13650704956054687500000\) | \(3578450400000000000000000000\) | \([2]\) | \(117964800\) | \(4.0279\) | |
154560.n3 | 154560dp2 | \([0, -1, 0, -154886401, -619565493599]\) | \(1567558142704512417614401/274462175610000000000\) | \(71948612563107840000000000\) | \([2, 2]\) | \(58982400\) | \(3.6813\) | |
154560.n4 | 154560dp1 | \([0, -1, 0, 18456319, -55473614175]\) | \(2652277923951208297919/6605028468326400000\) | \(-1731468582800955801600000\) | \([2]\) | \(29491200\) | \(3.3348\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 154560.n have rank \(0\).
Complex multiplication
The elliptic curves in class 154560.n do not have complex multiplication.Modular form 154560.2.a.n
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.