Properties

Label 3675.h
Number of curves $2$
Conductor $3675$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands for: SageMath
sage: E = EllipticCurve("h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3675.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3675.h1 3675a2 \([0, -1, 1, -251533, -48572532]\) \(-19539165184/46875\) \(-4222266357421875\) \([]\) \(24192\) \(1.8776\)  
3675.h2 3675a1 \([0, -1, 1, 5717, -338157]\) \(229376/675\) \(-60800635546875\) \([]\) \(8064\) \(1.3283\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 3675.h have rank \(1\).

Complex multiplication

The elliptic curves in class 3675.h do not have complex multiplication.

Modular form 3675.2.a.h

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2q^{4} + q^{9} + 2q^{12} + q^{13} + 4q^{16} - 6q^{17} + 5q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.