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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 3744.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3744.n1 | 3744a2 | \([0, 0, 0, -204, -1120]\) | \(8489664/13\) | \(1437696\) | \([2]\) | \(512\) | \(0.081110\) | |
3744.n2 | 3744a1 | \([0, 0, 0, -9, -28]\) | \(-46656/169\) | \(-292032\) | \([2]\) | \(256\) | \(-0.26546\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3744.n have rank \(0\).
Complex multiplication
The elliptic curves in class 3744.n do not have complex multiplication.Modular form 3744.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.