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Properties

Label 276138.m
Number of curves $2$
Conductor $276138$
CM no
Rank $1$
Graph

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

Elliptic curves in class 276138.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
276138.m1 276138m2 \([1, -1, 0, -30998970, -66617297046]\) \(-30526075007211889/103499257854\) \(-11169449787850442088174\) \([]\) \(19317760\) \(3.0947\)  
276138.m2 276138m1 \([1, -1, 0, -4860, 45034704]\) \(-117649/8118144\) \(-876095188107041664\) \([]\) \(2759680\) \(2.1217\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 276138.m have rank \(1\).

Complex multiplication

The elliptic curves in class 276138.m do not have complex multiplication.

Modular form 276138.2.a.m

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - q^{7} - q^{8} + q^{10} - 2 q^{11} + q^{14} + q^{16} - 3 q^{17} + q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.