Properties

Label 13860.m
Number of curves $2$
Conductor $13860$
CM no
Rank $1$
Graph

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

Elliptic curves in class 13860.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
13860.m1 13860p2 \([0, 0, 0, -887575503, 10152728950502]\) \(414354576760345737269208016/1182266314178222109375\) \(220639268617196522940000000\) \([2]\) \(6988800\) \(3.9263\)  
13860.m2 13860p1 \([0, 0, 0, -33278628, 286796059877]\) \(-349439858058052607328256/2844147488104248046875\) \(-33174136301247949218750000\) \([2]\) \(3494400\) \(3.5798\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 13860.m have rank \(1\).

Complex multiplication

The elliptic curves in class 13860.m do not have complex multiplication.

Modular form 13860.2.a.m

sage: E.q_eigenform(10)
 
\(q - q^{5} + q^{7} + q^{11} + 4q^{13} - 2q^{17} + 2q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.