Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 7605.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7605.j1 | 7605a1 | \([0, 0, 1, -7098, 231234]\) | \(-303464448/1625\) | \(-211776244875\) | \([]\) | \(8064\) | \(1.0178\) | \(\Gamma_0(N)\)-optimal |
7605.j2 | 7605a2 | \([0, 0, 1, 18252, 1230869]\) | \(7077888/10985\) | \(-1043641805793795\) | \([]\) | \(24192\) | \(1.5671\) |
Rank
sage: E.rank()
The elliptic curves in class 7605.j have rank \(1\).
Complex multiplication
The elliptic curves in class 7605.j do not have complex multiplication.Modular form 7605.2.a.j
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.