↑

Properties

Label 1421d
Number of curves $2$
Conductor $1421$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 1421d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1421.g2 1421d1 \([1, 0, 1, -467, -4119]\) \(-95443993/5887\) \(-692599663\) \([2]\) \(576\) \(0.45075\) \(\Gamma_0(N)\)-optimal
1421.g1 1421d2 \([1, 0, 1, -7572, -254215]\) \(408023180713/1421\) \(167179229\) \([2]\) \(1152\) \(0.79732\)  

Rank

sage: E.rank()
 

The elliptic curves in class 1421d have rank \(0\).

Complex multiplication

The elliptic curves in class 1421d do not have complex multiplication.

Modular form 1421.2.a.d

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