↑

Properties

Label 367575bl
Number of curves $2$
Conductor $367575$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("bl1")
 
E.isogeny_class()
 

Elliptic curves in class 367575bl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
367575.bl2 367575bl1 \([1, 1, 0, -3045, 28800]\) \(5177717/2349\) \(1417271792625\) \([2]\) \(414720\) \(1.0268\) \(\Gamma_0(N)\)-optimal
367575.bl1 367575bl2 \([1, 1, 0, -41070, 3184875]\) \(12698260037/7569\) \(4566764665125\) \([2]\) \(829440\) \(1.3733\)  

Rank

sage: E.rank()
 

The elliptic curves in class 367575bl have rank \(1\).

Complex multiplication

The elliptic curves in class 367575bl do not have complex multiplication.

Modular form 367575.2.a.bl

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} - q^{4} - q^{6} - 2 q^{7} - 3 q^{8} + q^{9} + q^{12} - 2 q^{14} - q^{16} - 2 q^{17} + q^{18} + O(q^{20})\) 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.