Properties

Label 309168.d
Number of curves $2$
Conductor $309168$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 309168.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
309168.d1 309168d1 \([0, 0, 0, -71263227, -136593274070]\) \(13403946614821979039929/5057590268826067968\) \(15101883621270337735360512\) \([2]\) \(121405440\) \(3.5310\) \(\Gamma_0(N)\)-optimal
309168.d2 309168d2 \([0, 0, 0, 222934533, -974762692310]\) \(410363075617640914325831/374944243169850027552\) \(-1119577510997281464669831168\) \([2]\) \(242810880\) \(3.8775\)  

Rank

sage: E.rank()
 

The elliptic curves in class 309168.d have rank \(1\).

Complex multiplication

The elliptic curves in class 309168.d do not have complex multiplication.

Modular form 309168.2.a.d

sage: E.q_eigenform(10)
 
\(q - 4 q^{5} + 4 q^{7} + 6 q^{17} - q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.