Properties

Label 225318g
Number of curves $2$
Conductor $225318$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 225318g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
225318.q2 225318g1 \([1, 1, 1, -29912115, 67425426801]\) \(-274585709373920209/23361765507072\) \(-251821500866333960306688\) \([2]\) \(50872320\) \(3.2351\) \(\Gamma_0(N)\)-optimal
225318.q1 225318g2 \([1, 1, 1, -487970355, 4148724345201]\) \(1192111508635128247249/7651496452608\) \(82477127851741275628032\) \([2]\) \(101744640\) \(3.5817\)  

Rank

sage: E.rank()
 

The elliptic curves in class 225318g have rank \(1\).

Complex multiplication

The elliptic curves in class 225318g do not have complex multiplication.

Modular form 225318.2.a.g

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - 4 q^{5} - q^{6} + q^{8} + q^{9} - 4 q^{10} + 2 q^{11} - q^{12} - 4 q^{13} + 4 q^{15} + q^{16} - q^{17} + q^{18} - 6 q^{19} + O(q^{20})\) 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.