↑

Properties

Label 121242m
Number of curves $2$
Conductor $121242$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 121242m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
121242.k1 121242m1 \([1, 0, 1, -3580518021, -82464771413840]\) \(2865531538344235202493486625/162273239306145792\) \(287476942098434945421312\) \([2]\) \(68544000\) \(3.9680\) \(\Gamma_0(N)\)-optimal
121242.k2 121242m2 \([1, 0, 1, -3574051781, -82777460674768]\) \(-2850034530503997051617454625/21567731878730391026112\) \(-38208552654815490256610000832\) \([2]\) \(137088000\) \(4.3146\)  

Rank

sage: E.rank()
 

The elliptic curves in class 121242m have rank \(0\).

Complex multiplication

The elliptic curves in class 121242m do not have complex multiplication.

Modular form 121242.2.a.m

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