Properties

Label 1248g
Number of curves $2$
Conductor $1248$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1248g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1248.c2 1248g1 \([0, -1, 0, -18, 36]\) \(10648000/117\) \(7488\) \([2]\) \(64\) \(-0.44189\) \(\Gamma_0(N)\)-optimal
1248.c1 1248g2 \([0, -1, 0, -33, -15]\) \(1000000/507\) \(2076672\) \([2]\) \(128\) \(-0.095314\)  

Rank

sage: E.rank()
 

The elliptic curves in class 1248g have rank \(1\).

Complex multiplication

The elliptic curves in class 1248g do not have complex multiplication.

Modular form 1248.2.a.g

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