Properties

Label 3850.t
Number of curves $4$
Conductor $3850$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("t1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3850.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3850.t1 3850s3 \([1, -1, 1, -81666730, -284043362603]\) \(3855131356812007128171561/8967612500\) \(140118945312500\) \([2]\) \(245760\) \(2.8447\)  
3850.t2 3850s4 \([1, -1, 1, -5373730, -3942310603]\) \(1098325674097093229481/205612182617187500\) \(3212690353393554687500\) \([2]\) \(245760\) \(2.8447\)  
3850.t3 3850s2 \([1, -1, 1, -5104230, -4437112603]\) \(941226862950447171561/45393906250000\) \(709279785156250000\) \([2, 2]\) \(122880\) \(2.4982\)  
3850.t4 3850s1 \([1, -1, 1, -302230, -76896603]\) \(-195395722614328041/50730248800000\) \(-792660137500000000\) \([4]\) \(61440\) \(2.1516\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 3850.t have rank \(1\).

Complex multiplication

The elliptic curves in class 3850.t do not have complex multiplication.

Modular form 3850.2.a.t

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{7} + q^{8} - 3q^{9} - q^{11} - 2q^{13} + q^{14} + q^{16} - 6q^{17} - 3q^{18} + 4q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.