Properties

Label 448.f
Number of curves $2$
Conductor $448$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 448.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
448.f1 448d2 \([0, -1, 0, -33, -31]\) \(125000/49\) \(1605632\) \([2]\) \(64\) \(-0.11063\)  
448.f2 448d1 \([0, -1, 0, 7, -7]\) \(8000/7\) \(-28672\) \([2]\) \(32\) \(-0.45720\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 448.f have rank \(0\).

Complex multiplication

The elliptic curves in class 448.f do not have complex multiplication.

Modular form 448.2.a.f

sage: E.q_eigenform(10)
 
\(q + 2q^{3} - q^{7} + q^{9} + 4q^{11} + 4q^{13} - 2q^{17} + 6q^{19} + O(q^{20})\)  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.