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Properties

Label 308898ba
Number of curves $2$
Conductor $308898$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ba1")
 
E.isogeny_class()
 

Elliptic curves in class 308898ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
308898.ba1 308898ba1 \([1, -1, 1, -10969097, -13911184695]\) \(39616946929/226368\) \(834008229559914426432\) \([2]\) \(39536640\) \(2.8559\) \(\Gamma_0(N)\)-optimal
308898.ba2 308898ba2 \([1, -1, 1, -4791137, -29491999815]\) \(-3301293169/100082952\) \(-368735888494177165786248\) \([2]\) \(79073280\) \(3.2024\)  

Rank

sage: E.rank()
 

The elliptic curves in class 308898ba have rank \(0\).

Complex multiplication

The elliptic curves in class 308898ba do not have complex multiplication.

Modular form 308898.2.a.ba

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - 4 q^{5} - 4 q^{7} + q^{8} - 4 q^{10} + 6 q^{13} - 4 q^{14} + q^{16} - 2 q^{17} - 4 q^{19} + O(q^{20})\) 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 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.