Properties

Label 900.d
Number of curves $2$
Conductor $900$
CM \(\Q(\sqrt{-3}) \)
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 900.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality CM discriminant
900.d1 900c2 \([0, 0, 0, 0, -2700]\) \(0\) \(-3149280000\) \([]\) \(432\) \(0.50142\)   \(-3\)
900.d2 900c1 \([0, 0, 0, 0, 100]\) \(0\) \(-4320000\) \([3]\) \(144\) \(-0.047887\) \(\Gamma_0(N)\)-optimal \(-3\)

Rank

sage: E.rank()
 

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

Complex multiplication

Each elliptic curve in class 900.d has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-3}) \).

Modular form 900.2.a.d

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