Properties

Label 99225j
Number of curves $2$
Conductor $99225$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 99225j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
99225.l2 99225j1 \([1, -1, 1, -230, -41478]\) \(-9/5\) \(-744497578125\) \([]\) \(95040\) \(0.95708\) \(\Gamma_0(N)\)-optimal
99225.l1 99225j2 \([1, -1, 1, -275855, 56075772]\) \(-15590912409/78125\) \(-11632774658203125\) \([]\) \(665280\) \(1.9300\)  

Rank

sage: E.rank()
 

The elliptic curves in class 99225j have rank \(0\).

Complex multiplication

The elliptic curves in class 99225j do not have complex multiplication.

Modular form 99225.2.a.j

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

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.