Properties

Label 900.b
Number of curves $4$
Conductor $900$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 900.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
900.b1 900e3 \([0, 0, 0, -9300, 345125]\) \(488095744/125\) \(22781250000\) \([2]\) \(864\) \(0.97338\)  
900.b2 900e4 \([0, 0, 0, -8175, 431750]\) \(-20720464/15625\) \(-45562500000000\) \([2]\) \(1728\) \(1.3200\)  
900.b3 900e1 \([0, 0, 0, -300, -1375]\) \(16384/5\) \(911250000\) \([2]\) \(288\) \(0.42408\) \(\Gamma_0(N)\)-optimal
900.b4 900e2 \([0, 0, 0, 825, -9250]\) \(21296/25\) \(-72900000000\) \([2]\) \(576\) \(0.77065\)  

Rank

sage: E.rank()
 

The elliptic curves in class 900.b have rank \(1\).

Complex multiplication

The elliptic curves in class 900.b do not have complex multiplication.

Modular form 900.2.a.b

sage: E.q_eigenform(10)
 
\(q - 2q^{7} - 2q^{13} - 6q^{17} - 4q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.