Properties

Label 312.c
Number of curves $2$
Conductor $312$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 312.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
312.c1 312e1 \([0, -1, 0, -651, 6228]\) \(1909913257984/129730653\) \(2075690448\) \([2]\) \(240\) \(0.53639\) \(\Gamma_0(N)\)-optimal
312.c2 312e2 \([0, -1, 0, 564, 25668]\) \(77366117936/1172914587\) \(-300266134272\) \([2]\) \(480\) \(0.88296\)  

Rank

sage: E.rank()
 

The elliptic curves in class 312.c have rank \(0\).

Complex multiplication

The elliptic curves in class 312.c do not have complex multiplication.

Modular form 312.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{3} + 4 q^{5} + q^{9} - 2 q^{11} - q^{13} - 4 q^{15} + 2 q^{17} + 8 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.