Properties

Label 303600i
Number of curves $4$
Conductor $303600$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 303600i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
303600.i3 303600i1 \([0, -1, 0, -15383, -719238]\) \(1610404796416/25255725\) \(6313931250000\) \([2]\) \(786432\) \(1.2569\) \(\Gamma_0(N)\)-optimal
303600.i2 303600i2 \([0, -1, 0, -30508, 944512]\) \(785089500496/360050625\) \(1440202500000000\) \([2, 2]\) \(1572864\) \(1.6035\)  
303600.i1 303600i3 \([0, -1, 0, -410008, 101132512]\) \(476411000270404/296484375\) \(4743750000000000\) \([2]\) \(3145728\) \(1.9501\)  
303600.i4 303600i4 \([0, -1, 0, 106992, 6994512]\) \(8465518982876/6233458275\) \(-99735332400000000\) \([2]\) \(3145728\) \(1.9501\)  

Rank

sage: E.rank()
 

The elliptic curves in class 303600i have rank \(1\).

Complex multiplication

The elliptic curves in class 303600i do not have complex multiplication.

Modular form 303600.2.a.i

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.