Properties

Label 9360.m
Number of curves $2$
Conductor $9360$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 9360.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9360.m1 9360c2 \([0, 0, 0, -5643, -162918]\) \(492983766/845\) \(34062612480\) \([2]\) \(9216\) \(0.91535\)  
9360.m2 9360c1 \([0, 0, 0, -243, -4158]\) \(-78732/325\) \(-6550502400\) \([2]\) \(4608\) \(0.56877\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 9360.m have rank \(0\).

Complex multiplication

The elliptic curves in class 9360.m do not have complex multiplication.

Modular form 9360.2.a.m

sage: E.q_eigenform(10)
 
\(q - q^{5} + q^{13} + 6 q^{17} + 8 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.