Properties

Label 2898.p
Number of curves $2$
Conductor $2898$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2898.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2898.p1 2898t2 \([1, -1, 1, -5450, -143607]\) \(24553362849625/1755162752\) \(1279513646208\) \([2]\) \(5376\) \(1.0701\)  
2898.p2 2898t1 \([1, -1, 1, 310, -9975]\) \(4533086375/60669952\) \(-44228395008\) \([2]\) \(2688\) \(0.72349\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2898.p have rank \(1\).

Complex multiplication

The elliptic curves in class 2898.p do not have complex multiplication.

Modular form 2898.2.a.p

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{7} + q^{8} - 4q^{11} + q^{14} + q^{16} - 6q^{17} - 6q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.