Show commands:
SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 7350.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7350.o1 | 7350d1 | \([1, 1, 0, -18400, 359500]\) | \(1092727/540\) | \(340483559062500\) | \([2]\) | \(32256\) | \(1.4815\) | \(\Gamma_0(N)\)-optimal |
7350.o2 | 7350d2 | \([1, 1, 0, 67350, 2846250]\) | \(53582633/36450\) | \(-22982640236718750\) | \([2]\) | \(64512\) | \(1.8281\) |
Rank
sage: E.rank()
The elliptic curves in class 7350.o have rank \(0\).
Complex multiplication
The elliptic curves in class 7350.o do not have complex multiplication.Modular form 7350.2.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 LMFDB 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 LMFDB labels.