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SageMath
E = EllipticCurve("fu1")
E.isogeny_class()
Elliptic curves in class 37440.fu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
37440.fu1 | 37440ck4 | \([0, 0, 0, -299532, -63097616]\) | \(31103978031362/195\) | \(18632540160\) | \([2]\) | \(196608\) | \(1.5763\) | |
37440.fu2 | 37440ck3 | \([0, 0, 0, -25932, -158096]\) | \(20183398562/11567205\) | \(1105263649751040\) | \([2]\) | \(196608\) | \(1.5763\) | |
37440.fu3 | 37440ck2 | \([0, 0, 0, -18732, -984656]\) | \(15214885924/38025\) | \(1816672665600\) | \([2, 2]\) | \(98304\) | \(1.2297\) | |
37440.fu4 | 37440ck1 | \([0, 0, 0, -732, -27056]\) | \(-3631696/24375\) | \(-291133440000\) | \([2]\) | \(49152\) | \(0.88311\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 37440.fu have rank \(1\).
Complex multiplication
The elliptic curves in class 37440.fu do not have complex multiplication.Modular form 37440.2.a.fu
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.