Properties

Label 249090c
Number of curves $2$
Conductor $249090$
CM no
Rank $1$
Graph

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

Elliptic curves in class 249090c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
249090.c2 249090c1 \([1, 1, 0, -1057067933, -13229078435607]\) \(-2776583906674595739386209/93760019539193340\) \(-4411022721798564709632540\) \([2]\) \(152064000\) \(3.8210\) \(\Gamma_0(N)\)-optimal
249090.c1 249090c2 \([1, 1, 0, -16913224003, -846625470243593]\) \(11373164188748320280858647489/12968007753150\) \(610091349561772275150\) \([2]\) \(304128000\) \(4.1676\)  

Rank

sage: E.rank()
 

The elliptic curves in class 249090c have rank \(1\).

Complex multiplication

The elliptic curves in class 249090c do not have complex multiplication.

Modular form 249090.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - 4 q^{7} - q^{8} + q^{9} + q^{10} + 2 q^{11} - q^{12} + 4 q^{14} + q^{15} + q^{16} - 2 q^{17} - q^{18} + O(q^{20})\) 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 Cremona 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 Cremona labels.