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Properties

Label 455175ba
Number of curves $2$
Conductor $455175$
CM no
Rank $1$
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Show commands: SageMath
E = EllipticCurve("ba1")
 
E.isogeny_class()
 

Elliptic curves in class 455175ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
455175.ba1 455175ba1 \([1, -1, 1, -1171805, -472295428]\) \(5177717/189\) \(6495504676541015625\) \([2]\) \(9461760\) \(2.3794\) \(\Gamma_0(N)\)-optimal
455175.ba2 455175ba2 \([1, -1, 1, 453820, -1681760428]\) \(300763/35721\) \(-1227650383866251953125\) \([2]\) \(18923520\) \(2.7260\)  

Rank

sage: E.rank()
 

The elliptic curves in class 455175ba have rank \(1\).

Complex multiplication

The elliptic curves in class 455175ba do not have complex multiplication.

Modular form 455175.2.a.ba

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} - q^{7} + 3 q^{8} - 6 q^{11} + 2 q^{13} + q^{14} - q^{16} - 6 q^{19} + O(q^{20})\) 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.