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Properties

Label 2541.f
Number of curves $2$
Conductor $2541$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 2541.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2541.f1 2541k2 \([0, 1, 1, -40817, -3187585]\) \(35084566528/1029\) \(220575288549\) \([]\) \(6336\) \(1.2764\)  
2541.f2 2541k1 \([0, 1, 1, -887, 2822]\) \(360448/189\) \(40513828509\) \([3]\) \(2112\) \(0.72713\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2541.f have rank \(0\).

Complex multiplication

The elliptic curves in class 2541.f do not have complex multiplication.

Modular form 2541.2.a.f

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