↑

Properties

Label 446400.bc
Number of curves $2$
Conductor $446400$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
Copy content sage:E = EllipticCurve("bc1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 446400.bc have rank \(0\).

Complex multiplication

The elliptic curves in class 446400.bc do not have complex multiplication.

Modular form 446400.2.a.bc

Copy content sage:E.q_eigenform(10)
 
\(q - 4 q^{7} - 4 q^{11} + 4 q^{13} + 4 q^{17} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

Copy content 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

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 446400.bc

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
446400.bc1 446400bc1 \([0, 0, 0, -28200, -281000]\) \(212629504/120125\) \(1401138000000000\) \([2]\) \(2211840\) \(1.5963\) \(\Gamma_0(N)\)-optimal
446400.bc2 446400bc2 \([0, 0, 0, 111300, -2234000]\) \(817036976/484375\) \(-90396000000000000\) \([2]\) \(4423680\) \(1.9429\)