Properties

Label 28899c
Number of curves $3$
Conductor $28899$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 28899c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
28899.k3 28899c1 \([0, 0, 1, 1014, 549]\) \(32768/19\) \(-66856131459\) \([]\) \(17280\) \(0.76661\) \(\Gamma_0(N)\)-optimal
28899.k2 28899c2 \([0, 0, 1, -14196, 692604]\) \(-89915392/6859\) \(-24135063456699\) \([]\) \(51840\) \(1.3159\)  
28899.k1 28899c3 \([0, 0, 1, -1170156, 487207269]\) \(-50357871050752/19\) \(-66856131459\) \([]\) \(155520\) \(1.8652\)  

Rank

sage: E.rank()
 

The elliptic curves in class 28899c have rank \(0\).

Complex multiplication

The elliptic curves in class 28899c do not have complex multiplication.

Modular form 28899.2.a.c

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

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.