Properties

Label 222180g
Number of curves $2$
Conductor $222180$
CM no
Rank $1$
Graph

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

Elliptic curves in class 222180g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
222180.v2 222180g1 \([0, 1, 0, 9468395, 7378393175]\) \(2477112820760576/2053567248075\) \(-77824423216656937900800\) \([]\) \(20528640\) \(3.0801\) \(\Gamma_0(N)\)-optimal
222180.v1 222180g2 \([0, 1, 0, -200777365, 1110522127463]\) \(-23618971583050153984/391556092921875\) \(-14838874703118431532000000\) \([]\) \(61585920\) \(3.6294\)  

Rank

sage: E.rank()
 

The elliptic curves in class 222180g have rank \(1\).

Complex multiplication

The elliptic curves in class 222180g do not have complex multiplication.

Modular form 222180.2.a.g

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} - q^{7} + q^{9} + 3 q^{11} - 4 q^{13} + q^{15} - 6 q^{17} + q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.