Properties

Label 14112bb
Number of curves $4$
Conductor $14112$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("bb1")
 
E.isogeny_class()
 

Elliptic curves in class 14112bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14112.m3 14112bb1 \([0, 0, 0, -6321, 178360]\) \(5088448/441\) \(2420662999104\) \([2, 2]\) \(24576\) \(1.1171\) \(\Gamma_0(N)\)-optimal
14112.m2 14112bb2 \([0, 0, 0, -21756, -1031744]\) \(3241792/567\) \(199185983926272\) \([2]\) \(49152\) \(1.4636\)  
14112.m1 14112bb3 \([0, 0, 0, -98931, 11976874]\) \(2438569736/21\) \(922157332992\) \([2]\) \(49152\) \(1.4636\)  
14112.m4 14112bb4 \([0, 0, 0, 6909, 826630]\) \(830584/7203\) \(-316299965216256\) \([2]\) \(49152\) \(1.4636\)  

Rank

sage: E.rank()
 

The elliptic curves in class 14112bb have rank \(1\).

Complex multiplication

The elliptic curves in class 14112bb do not have complex multiplication.

Modular form 14112.2.a.bb

sage: E.q_eigenform(10)
 
\(q - 2 q^{5} - 4 q^{11} + 6 q^{13} - 2 q^{17} + 4 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.