Show commands:
SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 1134.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1134.a1 | 1134d2 | \([1, -1, 0, -96, -424]\) | \(-185193/56\) | \(-29760696\) | \([]\) | \(432\) | \(0.14804\) | |
1134.a2 | 1134d1 | \([1, -1, 0, 9, 3]\) | \(934407/686\) | \(-55566\) | \([3]\) | \(144\) | \(-0.40127\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1134.a have rank \(0\).
Complex multiplication
The elliptic curves in class 1134.a do not have complex multiplication.Modular form 1134.2.a.a
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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.