Show commands:
SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 279174o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
279174.o2 | 279174o1 | \([1, 1, 0, -305034159, -2479970838555]\) | \(-130039596910901639983897/34807971197715480576\) | \(-840179806534870054771359744\) | \([2]\) | \(143327232\) | \(3.8827\) | \(\Gamma_0(N)\)-optimal |
279174.o1 | 279174o2 | \([1, 1, 0, -5159124399, -142626293429787]\) | \(629155769689303170154943257/31962256000330424832\) | \(771491159603639652181713408\) | \([2]\) | \(286654464\) | \(4.2293\) |
Rank
sage: E.rank()
The elliptic curves in class 279174o have rank \(0\).
Complex multiplication
The elliptic curves in class 279174o do not have complex multiplication.Modular form 279174.2.a.o
sage: E.q_eigenform(10)
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.