Properties

Label 900.e
Number of curves $2$
Conductor $900$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 900.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
900.e1 900d2 \([0, 0, 0, -10920, 439220]\) \(-30866268160/3\) \(-13996800\) \([]\) \(864\) \(0.80452\)  
900.e2 900d1 \([0, 0, 0, -120, 740]\) \(-40960/27\) \(-125971200\) \([]\) \(288\) \(0.25522\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 900.2.a.e

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.