Properties

Label 78400.il
Number of curves $2$
Conductor $78400$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("il1")
 
E.isogeny_class()
 

Elliptic curves in class 78400.il

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
78400.il1 78400hi2 \([0, 1, 0, -3946133, -3018546637]\) \(-225637236736/1715\) \(-51652616960000000\) \([]\) \(1327104\) \(2.3818\)  
78400.il2 78400hi1 \([0, 1, 0, -26133, -7986637]\) \(-65536/875\) \(-26353376000000000\) \([]\) \(442368\) \(1.8325\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 78400.il have rank \(1\).

Complex multiplication

The elliptic curves in class 78400.il do not have complex multiplication.

Modular form 78400.2.a.il

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{9} + 3 q^{11} + q^{13} - 3 q^{17} - 2 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.