Properties

Label 121275gi
Number of curves $2$
Conductor $121275$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("gi1")
 
E.isogeny_class()
 

Elliptic curves in class 121275gi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
121275.dy1 121275gi1 \([0, 0, 1, -257250, 52682656]\) \(-56197120/3267\) \(-109452311448046875\) \([]\) \(1088640\) \(2.0258\) \(\Gamma_0(N)\)-optimal
121275.dy2 121275gi2 \([0, 0, 1, 1396500, 93199531]\) \(8990228480/5314683\) \(-178054587990094921875\) \([]\) \(3265920\) \(2.5751\)  

Rank

sage: E.rank()
 

The elliptic curves in class 121275gi have rank \(1\).

Complex multiplication

The elliptic curves in class 121275gi do not have complex multiplication.

Modular form 121275.2.a.gi

sage: E.q_eigenform(10)
 
\(q - 2 q^{4} + q^{11} + q^{13} + 4 q^{16} - 6 q^{17} + 7 q^{19} + O(q^{20})\) 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.