Properties

Label 25200eq
Number of curves $3$
Conductor $25200$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands for: SageMath
sage: E = EllipticCurve("eq1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 25200eq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
25200.dn2 25200eq1 \([0, 0, 0, -4800, 142000]\) \(-262144/35\) \(-1632960000000\) \([]\) \(34560\) \(1.0760\) \(\Gamma_0(N)\)-optimal
25200.dn3 25200eq2 \([0, 0, 0, 31200, -362000]\) \(71991296/42875\) \(-2000376000000000\) \([]\) \(103680\) \(1.6253\)  
25200.dn1 25200eq3 \([0, 0, 0, -472800, -130898000]\) \(-250523582464/13671875\) \(-637875000000000000\) \([]\) \(311040\) \(2.1746\)  

Rank

sage: E.rank()
 

The elliptic curves in class 25200eq have rank \(0\).

Complex multiplication

The elliptic curves in class 25200eq do not have complex multiplication.

Modular form 25200.2.a.eq

sage: E.q_eigenform(10)
 
\(q + q^{7} - 3q^{11} - 5q^{13} + 3q^{17} - 2q^{19} + O(q^{20})\)  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 Cremona numbering.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.