Properties

Label 262080.c
Number of curves $4$
Conductor $262080$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 262080.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
262080.c1 262080c3 \([0, 0, 0, -29648748, -62138026928]\) \(15082569606665230489/7751016000\) \(1481242224623616000\) \([2]\) \(15925248\) \(2.8187\)  
262080.c2 262080c4 \([0, 0, 0, -29487468, -62847465392]\) \(-14837772556740428569/342100087875000\) \(-65376344882774016000000\) \([2]\) \(31850496\) \(3.1652\)  
262080.c3 262080c1 \([0, 0, 0, -436908, -49912112]\) \(48264326765929/22299191460\) \(4261441850399784960\) \([2]\) \(5308416\) \(2.2694\) \(\Gamma_0(N)\)-optimal
262080.c4 262080c2 \([0, 0, 0, 1538772, -376294448]\) \(2108526614950391/1540302022350\) \(-294356300409903513600\) \([2]\) \(10616832\) \(2.6159\)  

Rank

sage: E.rank()
 

The elliptic curves in class 262080.c have rank \(1\).

Complex multiplication

The elliptic curves in class 262080.c do not have complex multiplication.

Modular form 262080.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{5} - q^{7} - 6 q^{11} - q^{13} + 8 q^{19} + O(q^{20})\) Copy content Toggle raw display

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.