Properties

Label 74060.m
Number of curves $2$
Conductor $74060$
CM no
Rank $1$
Graph

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

Elliptic curves in class 74060.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
74060.m1 74060d1 \([0, 1, 0, -1392756666, -20006497323991]\) \(-126142795384287538429696/9315359375\) \(-22064120102921750000\) \([]\) \(18703872\) \(3.6080\) \(\Gamma_0(N)\)-optimal
74060.m2 74060d2 \([0, 1, 0, -1378738166, -20428936569091]\) \(-122372013839654770813696/5297595236711512175\) \(-12547747526860066261767177200\) \([]\) \(56111616\) \(4.1573\)  

Rank

sage: E.rank()
 

The elliptic curves in class 74060.m have rank \(1\).

Complex multiplication

The elliptic curves in class 74060.m do not have complex multiplication.

Modular form 74060.2.a.m

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} - q^{7} - 2 q^{9} + 6 q^{11} - q^{13} - q^{15} - 6 q^{17} - 2 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.