Properties

Label 48400cm
Number of curves $2$
Conductor $48400$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("cm1")
 
E.isogeny_class()
 

Elliptic curves in class 48400cm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
48400.t2 48400cm1 \([0, 1, 0, 144192, 8046388]\) \(24167/16\) \(-219503494144000000\) \([]\) \(456192\) \(2.0163\) \(\Gamma_0(N)\)-optimal
48400.t1 48400cm2 \([0, 1, 0, -2517808, 1578626388]\) \(-128667913/4096\) \(-56192894500864000000\) \([]\) \(1368576\) \(2.5656\)  

Rank

sage: E.rank()
 

The elliptic curves in class 48400cm have rank \(1\).

Complex multiplication

The elliptic curves in class 48400cm do not have complex multiplication.

Modular form 48400.2.a.cm

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} + 2 q^{7} + q^{9} - 5 q^{13} - 3 q^{17} - 2 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.