Show commands:
SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 50400bh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 50400.dn1 | 50400bh1 | \([0, 0, 0, -5925, -173000]\) | \(31554496/525\) | \(382725000000\) | \([2]\) | \(73728\) | \(1.0210\) | \(\Gamma_0(N)\)-optimal |
| 50400.dn2 | 50400bh2 | \([0, 0, 0, -300, -488000]\) | \(-64/2205\) | \(-102876480000000\) | \([2]\) | \(147456\) | \(1.3676\) |
Rank
sage: E.rank()
The elliptic curves in class 50400bh have rank \(1\).
Complex multiplication
The elliptic curves in class 50400bh do not have complex multiplication.Modular form 50400.2.a.bh
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.
