Properties

Label 1386.c
Number of curves $4$
Conductor $1386$
CM no
Rank $0$
Graph

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

Elliptic curves in class 1386.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1386.c1 1386d4 \([1, -1, 0, -127197, 17491383]\) \(312196988566716625/25367712678\) \(18493062542262\) \([6]\) \(4608\) \(1.5909\)  
1386.c2 1386d3 \([1, -1, 0, -7407, 313497]\) \(-61653281712625/21875235228\) \(-15947046481212\) \([6]\) \(2304\) \(1.2443\)  
1386.c3 1386d2 \([1, -1, 0, -3267, -35235]\) \(5290763640625/2291573592\) \(1670557148568\) \([2]\) \(1536\) \(1.0416\)  
1386.c4 1386d1 \([1, -1, 0, 693, -4347]\) \(50447927375/39517632\) \(-28808353728\) \([2]\) \(768\) \(0.69498\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1386.c have rank \(0\).

Complex multiplication

The elliptic curves in class 1386.c do not have complex multiplication.

Modular form 1386.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{7} - q^{8} + q^{11} + 2q^{13} - q^{14} + q^{16} + 2q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.