Properties

Label 94136.b
Number of curves $2$
Conductor $94136$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 94136.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
94136.b1 94136a2 \([0, 1, 0, -67800, -6736016]\) \(3543122/49\) \(476682460792832\) \([2]\) \(563200\) \(1.6221\)  
94136.b2 94136a1 \([0, 1, 0, -560, -280976]\) \(-4/7\) \(-34048747199488\) \([2]\) \(281600\) \(1.2755\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 94136.b have rank \(1\).

Complex multiplication

The elliptic curves in class 94136.b do not have complex multiplication.

Modular form 94136.2.a.b

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} - 4 q^{5} - q^{7} + q^{9} + 8 q^{15} + 2 q^{17} + 2 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.