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Properties

Label 454597d
Number of curves $2$
Conductor $454597$
CM no
Rank $1$
Graph

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

Elliptic curves in class 454597d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
454597.d1 454597d1 \([1, 0, 0, -2081384, -1155833777]\) \(23320116793/2873\) \(122852858289475457\) \([2]\) \(7464960\) \(2.3025\) \(\Gamma_0(N)\)-optimal
454597.d2 454597d2 \([1, 0, 0, -1906539, -1357989566]\) \(-17923019113/8254129\) \(-352956261865662987961\) \([2]\) \(14929920\) \(2.6491\)  

Rank

sage: E.rank()
 

The elliptic curves in class 454597d have rank \(1\).

Complex multiplication

The elliptic curves in class 454597d do not have complex multiplication.

Modular form 454597.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{2} - 2 q^{3} - q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{7} + 3 q^{8} + q^{9} + 2 q^{10} + 2 q^{12} + q^{13} - 2 q^{14} + 4 q^{15} - q^{16} - q^{18} - 4 q^{19} + O(q^{20})\) 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 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.