Show commands:
SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 28050.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
28050.b1 | 28050q1 | \([1, 1, 0, -7025, 268125]\) | \(-2454365649169/610929000\) | \(-9545765625000\) | \([]\) | \(114048\) | \(1.2085\) | \(\Gamma_0(N)\)-optimal |
28050.b2 | 28050q2 | \([1, 1, 0, 50725, -1868625]\) | \(923754305147471/633316406250\) | \(-9895568847656250\) | \([]\) | \(342144\) | \(1.7579\) |
Rank
sage: E.rank()
The elliptic curves in class 28050.b have rank \(1\).
Complex multiplication
The elliptic curves in class 28050.b do not have complex multiplication.Modular form 28050.2.a.b
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.