↑

Properties

Label 327015.m
Number of curves $2$
Conductor $327015$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 327015.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
327015.m1 327015m2 \([1, -1, 1, -125768, 17139412]\) \(2315685267/9245\) \(878331223902015\) \([2]\) \(1769472\) \(1.7242\)  
327015.m2 327015m1 \([1, -1, 1, -11693, -17468]\) \(1860867/1075\) \(102131537663025\) \([2]\) \(884736\) \(1.3776\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 327015.m have rank \(1\).

Complex multiplication

The elliptic curves in class 327015.m do not have complex multiplication.

Modular form 327015.2.a.m

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} - q^{5} + 4 q^{7} + 3 q^{8} + q^{10} - 4 q^{14} - q^{16} + 2 q^{17} - 6 q^{19} + O(q^{20})\) 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.