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Properties

Label 378.g
Number of curves $3$
Conductor $378$
CM no
Rank $0$
Graph

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

Elliptic curves in class 378.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
378.g1 378e2 \([1, -1, 1, -1271, -17117]\) \(-11527859979/28\) \(-551124\) \([]\) \(216\) \(0.34195\)  
378.g2 378e1 \([1, -1, 1, -11, -37]\) \(-5000211/21952\) \(-592704\) \([3]\) \(72\) \(-0.20736\) \(\Gamma_0(N)\)-optimal
378.g3 378e3 \([1, -1, 1, 94, 929]\) \(381790581/1835008\) \(-445906944\) \([3]\) \(216\) \(0.34195\)  

Rank

sage: E.rank()
 

The elliptic curves in class 378.g have rank \(0\).

Complex multiplication

The elliptic curves in class 378.g do not have complex multiplication.

Modular form 378.2.a.g

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + 3 q^{5} + q^{7} + q^{8} + 3 q^{10} - 3 q^{11} - 4 q^{13} + q^{14} + q^{16} + 6 q^{17} - 7 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.