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Properties

Label 290145.g
Number of curves $4$
Conductor $290145$
CM no
Rank $1$
Graph

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

Elliptic curves in class 290145.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
290145.g1 290145g3 \([1, 1, 1, -25342291, 49074312284]\) \(3026030815665395929/1364501953125\) \(811637583268798828125\) \([2]\) \(26880000\) \(2.9699\)  
290145.g2 290145g4 \([1, 1, 1, -13929921, -19669007532]\) \(502552788401502649/10024505152875\) \(5962809446414720197875\) \([2]\) \(26880000\) \(2.9699\)  
290145.g3 290145g2 \([1, 1, 1, -1840546, 500905718]\) \(1159246431432649/488076890625\) \(290319516984916265625\) \([2, 2]\) \(13440000\) \(2.6233\)  
290145.g4 290145g1 \([1, 1, 1, 383899, 57796274]\) \(10519294081031/8500170375\) \(-5056099571523315375\) \([2]\) \(6720000\) \(2.2768\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 290145.g have rank \(1\).

Complex multiplication

The elliptic curves in class 290145.g do not have complex multiplication.

Modular form 290145.2.a.g

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} - q^{4} - q^{5} + q^{6} + 4 q^{7} + 3 q^{8} + q^{9} + q^{10} - 4 q^{11} + q^{12} + 6 q^{13} - 4 q^{14} + q^{15} - q^{16} + 2 q^{17} - q^{18} + 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.