Properties

Label 265200g
Number of curves $4$
Conductor $265200$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 265200g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
265200.g3 265200g1 \([0, -1, 0, -1292008, -311097488]\) \(3726830856733921/1501644718080\) \(96105261957120000000\) \([2]\) \(10616832\) \(2.5323\) \(\Gamma_0(N)\)-optimal
265200.g2 265200g2 \([0, -1, 0, -9484008, 11026630512]\) \(1474074790091785441/32813650022400\) \(2100073601433600000000\) \([2, 2]\) \(21233664\) \(2.8789\)  
265200.g1 265200g3 \([0, -1, 0, -150924008, 713700550512]\) \(5940441603429810927841/3044264109120\) \(194832902983680000000\) \([2]\) \(42467328\) \(3.2254\)  
265200.g4 265200g4 \([0, -1, 0, 883992, 33836230512]\) \(1193680917131039/7728836230440000\) \(-494645518748160000000000\) \([2]\) \(42467328\) \(3.2254\)  

Rank

sage: E.rank()
 

The elliptic curves in class 265200g have rank \(0\).

Complex multiplication

The elliptic curves in class 265200g do not have complex multiplication.

Modular form 265200.2.a.g

sage: E.q_eigenform(10)
 
\(q - q^{3} - 4 q^{7} + q^{9} + 4 q^{11} - q^{13} - q^{17} - 8 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.