Properties

Label 144900m
Number of curves $2$
Conductor $144900$
CM no
Rank $0$
Graph

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

Elliptic curves in class 144900m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
144900.j2 144900m1 \([0, 0, 0, 240, 1325]\) \(1048576/1127\) \(-1643166000\) \([2]\) \(69120\) \(0.45496\) \(\Gamma_0(N)\)-optimal
144900.j1 144900m2 \([0, 0, 0, -1335, 12350]\) \(11279504/3703\) \(86383584000\) \([2]\) \(138240\) \(0.80153\)  

Rank

sage: E.rank()
 

The elliptic curves in class 144900m have rank \(0\).

Complex multiplication

The elliptic curves in class 144900m do not have complex multiplication.

Modular form 144900.2.a.m

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.