Properties

Label 312.f
Number of curves 4
Conductor 312
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("312.f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 312.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
312.f1 312c3 [0, 1, 0, -832, -9520] [2] 64  
312.f2 312c2 [0, 1, 0, -52, -160] [2, 2] 32  
312.f3 312c1 [0, 1, 0, -7, 2] [4] 16 \(\Gamma_0(N)\)-optimal
312.f4 312c4 [0, 1, 0, 8, -448] [2] 64  

Rank

sage: E.rank()
 

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

Modular form 312.2.a.f

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

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.