Properties

Label 303450.ec
Number of curves $2$
Conductor $303450$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("ec1")
 
E.isogeny_class()
 

Elliptic curves in class 303450.ec

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
303450.ec1 303450ec2 \([1, 1, 1, -46243763, -123841108969]\) \(-1159924308480625/31212514998\) \(-294294622823343696093750\) \([]\) \(44789760\) \(3.2851\)  
303450.ec2 303450ec1 \([1, 1, 1, 2524987, -690261469]\) \(188819819375/131167512\) \(-1236744090413409375000\) \([]\) \(14929920\) \(2.7358\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 303450.ec have rank \(1\).

Complex multiplication

The elliptic curves in class 303450.ec do not have complex multiplication.

Modular form 303450.2.a.ec

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{6} - q^{7} + q^{8} + q^{9} - q^{12} - 4 q^{13} - q^{14} + q^{16} + q^{18} + 2 q^{19} + O(q^{20})\) 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 LMFDB 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 LMFDB labels.