Properties

Label 5445.c
Number of curves $8$
Conductor $5445$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5445.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5445.c1 5445g7 \([1, -1, 1, -2352263, -1388010918]\) \(1114544804970241/405\) \(523044527445\) \([2]\) \(40960\) \(2.0391\)  
5445.c2 5445g5 \([1, -1, 1, -147038, -21653508]\) \(272223782641/164025\) \(211833033615225\) \([2, 2]\) \(20480\) \(1.6926\)  
5445.c3 5445g8 \([1, -1, 1, -119813, -29940798]\) \(-147281603041/215233605\) \(-277967306709898245\) \([2]\) \(40960\) \(2.0391\)  
5445.c4 5445g4 \([1, -1, 1, -87143, 9923136]\) \(56667352321/15\) \(19372019535\) \([2]\) \(10240\) \(1.3460\)  
5445.c5 5445g3 \([1, -1, 1, -10913, -200208]\) \(111284641/50625\) \(65380565930625\) \([2, 2]\) \(10240\) \(1.3460\)  
5445.c6 5445g2 \([1, -1, 1, -5468, 154806]\) \(13997521/225\) \(290580293025\) \([2, 2]\) \(5120\) \(0.99940\)  
5445.c7 5445g1 \([1, -1, 1, -23, 6702]\) \(-1/15\) \(-19372019535\) \([2]\) \(2560\) \(0.65283\) \(\Gamma_0(N)\)-optimal
5445.c8 5445g6 \([1, -1, 1, 38092, -1533144]\) \(4733169839/3515625\) \(-4540317078515625\) \([2]\) \(20480\) \(1.6926\)  

Rank

sage: E.rank()
 

The elliptic curves in class 5445.c have rank \(1\).

Complex multiplication

The elliptic curves in class 5445.c do not have complex multiplication.

Modular form 5445.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} - q^{5} + 3q^{8} + q^{10} + 2q^{13} - q^{16} + 2q^{17} - 4q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 16 & 4 & 8 & 16 & 8 \\ 2 & 1 & 2 & 8 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 16 & 4 & 8 & 16 & 8 \\ 16 & 8 & 16 & 1 & 4 & 2 & 4 & 8 \\ 4 & 2 & 4 & 4 & 1 & 2 & 4 & 2 \\ 8 & 4 & 8 & 2 & 2 & 1 & 2 & 4 \\ 16 & 8 & 16 & 4 & 4 & 2 & 1 & 8 \\ 8 & 4 & 8 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.