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Properties

Label 2898.t
Number of curves $2$
Conductor $2898$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("t1")
 
E.isogeny_class()
 

Elliptic curves in class 2898.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2898.t1 2898m2 \([1, -1, 1, -100496, -12237101]\) \(-5702623460245179/252448\) \(-4968933984\) \([]\) \(15840\) \(1.3426\)  
2898.t2 2898m1 \([1, -1, 1, -1136, -19501]\) \(-5999796014211/2790817792\) \(-75352080384\) \([3]\) \(5280\) \(0.79333\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2898.t have rank \(0\).

Complex multiplication

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

Modular form 2898.2.a.t

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.