Show commands:
SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 9075g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9075.j2 | 9075g1 | \([0, -1, 1, -1283, 50093]\) | \(-123633664/492075\) | \(-930329296875\) | \([]\) | \(10368\) | \(0.98194\) | \(\Gamma_0(N)\)-optimal |
9075.j1 | 9075g2 | \([0, -1, 1, -149783, 22362218]\) | \(-196566176333824/421875\) | \(-797607421875\) | \([]\) | \(31104\) | \(1.5312\) |
Rank
sage: E.rank()
The elliptic curves in class 9075g have rank \(0\).
Complex multiplication
The elliptic curves in class 9075g do not have complex multiplication.Modular form 9075.2.a.g
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.