Properties

Label 3696m
Number of curves $2$
Conductor $3696$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 3696m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3696.b1 3696m1 \([0, -1, 0, -17242, -875009]\) \(-35431687725461248/440311012911\) \(-7044976206576\) \([]\) \(12960\) \(1.2758\) \(\Gamma_0(N)\)-optimal
3696.b2 3696m2 \([0, -1, 0, 59978, -4520981]\) \(1491325446082364672/1410025768453071\) \(-22560412295249136\) \([]\) \(38880\) \(1.8251\)  

Rank

sage: E.rank()
 

The elliptic curves in class 3696m have rank \(0\).

Complex multiplication

The elliptic curves in class 3696m do not have complex multiplication.

Modular form 3696.2.a.m

sage: E.q_eigenform(10)
 
\(q - q^{3} - 3 q^{5} - q^{7} + q^{9} - q^{11} - 7 q^{13} + 3 q^{15} - 6 q^{17} + q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.