Properties

Label 242550.md
Number of curves $4$
Conductor $242550$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("md1")
 
E.isogeny_class()
 

Elliptic curves in class 242550.md

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
242550.md1 242550md4 \([1, -1, 1, -287929130, -1827155344003]\) \(1969902499564819009/63690429687500\) \(85351267173751831054687500\) \([2]\) \(95551488\) \(3.7496\)  
242550.md2 242550md2 \([1, -1, 1, -39425630, 94446589997]\) \(5057359576472449/51765560000\) \(69370801290511875000000\) \([2]\) \(31850496\) \(3.2003\)  
242550.md3 242550md1 \([1, -1, 1, -617630, 3635869997]\) \(-19443408769/4249907200\) \(-5695282111780800000000\) \([2]\) \(15925248\) \(2.8538\) \(\Gamma_0(N)\)-optimal
242550.md4 242550md3 \([1, -1, 1, 5556370, -97938778003]\) \(14156681599871/3100231750000\) \(-4154607053102214843750000\) \([2]\) \(47775744\) \(3.4031\)  

Rank

sage: E.rank()
 

The elliptic curves in class 242550.md have rank \(1\).

Complex multiplication

The elliptic curves in class 242550.md do not have complex multiplication.

Modular form 242550.2.a.md

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{8} + q^{11} - 4 q^{13} + q^{16} + 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.