Show commands:
SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 334620u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
334620.u2 | 334620u1 | \([0, 0, 0, -2028, -569023]\) | \(-16384/2475\) | \(-139342252935600\) | \([2]\) | \(829440\) | \(1.3934\) | \(\Gamma_0(N)\)-optimal |
334620.u1 | 334620u2 | \([0, 0, 0, -116103, -15102178]\) | \(192143824/1815\) | \(1634949101111040\) | \([2]\) | \(1658880\) | \(1.7400\) |
Rank
sage: E.rank()
The elliptic curves in class 334620u have rank \(0\).
Complex multiplication
The elliptic curves in class 334620u do not have complex multiplication.Modular form 334620.2.a.u
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.