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Properties

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

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 290145.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
290145.i1 290145i3 \([1, 0, 0, -4657055, 3867737262]\) \(18778886261717401/732035835\) \(435431986465708035\) \([2]\) \(6451200\) \(2.4690\)  
290145.i2 290145i4 \([1, 0, 0, -1402385, -588117900]\) \(512787603508921/45649063125\) \(27153127328551138125\) \([2]\) \(6451200\) \(2.4690\)  
290145.i3 290145i2 \([1, 0, 0, -304880, 54361527]\) \(5268932332201/900900225\) \(535876463724147225\) \([2, 2]\) \(3225600\) \(2.1224\)  
290145.i4 290145i1 \([1, 0, 0, 35725, 4837560]\) \(8477185319/21880935\) \(-13015290423285135\) \([4]\) \(1612800\) \(1.7758\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 290145.2.a.i

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