Properties

Label 272832.m
Number of curves $2$
Conductor $272832$
CM no
Rank $0$
Graph

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

Elliptic curves in class 272832.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
272832.m1 272832m1 \([0, -1, 0, -24161377, 215512469761]\) \(-50577879066661513/621261297432576\) \(-19160306910925981961158656\) \([]\) \(69189120\) \(3.5330\) \(\Gamma_0(N)\)-optimal
272832.m2 272832m2 \([0, -1, 0, 215883743, -5587482288191]\) \(36079072622241241607/458176313589497856\) \(-14130606274639516994252046336\) \([]\) \(207567360\) \(4.0823\)  

Rank

sage: E.rank()
 

The elliptic curves in class 272832.m have rank \(0\).

Complex multiplication

The elliptic curves in class 272832.m do not have complex multiplication.

Modular form 272832.2.a.m

sage: E.q_eigenform(10)
 
\(q - q^{3} - 3 q^{5} + q^{9} + 6 q^{11} - 4 q^{13} + 3 q^{15} - 3 q^{17} + q^{19} + O(q^{20})\) 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.