Properties

Label 18480.cd
Number of curves $2$
Conductor $18480$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("cd1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 18480.cd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
18480.cd1 18480cs2 \([0, 1, 0, -516, -4680]\) \(59466754384/121275\) \(31046400\) \([2]\) \(7680\) \(0.32407\)  
18480.cd2 18480cs1 \([0, 1, 0, -21, -126]\) \(-67108864/343035\) \(-5488560\) \([2]\) \(3840\) \(-0.022504\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 18480.cd have rank \(0\).

Complex multiplication

The elliptic curves in class 18480.cd do not have complex multiplication.

Modular form 18480.2.a.cd

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} + q^{7} + q^{9} - q^{11} - 6q^{13} - q^{15} + 2q^{17} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.