Show commands:
SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 93138f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
93138.g1 | 93138f1 | \([1, 1, 0, -729, -1455]\) | \(912673/516\) | \(24275674596\) | \([2]\) | \(82944\) | \(0.68272\) | \(\Gamma_0(N)\)-optimal |
93138.g2 | 93138f2 | \([1, 1, 0, 2881, -7953]\) | \(56181887/33282\) | \(-1565781011442\) | \([2]\) | \(165888\) | \(1.0293\) |
Rank
sage: E.rank()
The elliptic curves in class 93138f have rank \(1\).
Complex multiplication
The elliptic curves in class 93138f do not have complex multiplication.Modular form 93138.2.a.f
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.