Properties

Label 87120.dd
Number of curves $2$
Conductor $87120$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("dd1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 87120.dd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
87120.dd1 87120fi2 \([0, 0, 0, -475167, -100817926]\) \(26962544/5625\) \(2475279168104160000\) \([2]\) \(1622016\) \(2.2444\)  
87120.dd2 87120fi1 \([0, 0, 0, 63888, -9502009]\) \(1048576/2025\) \(-55693781282343600\) \([2]\) \(811008\) \(1.8978\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 87120.dd have rank \(0\).

Complex multiplication

The elliptic curves in class 87120.dd do not have complex multiplication.

Modular form 87120.2.a.dd

sage: E.q_eigenform(10)
 
\(q + q^{5} - 4q^{7} - 4q^{13} + 4q^{19} + O(q^{20})\)  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.