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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 172480bf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 172480.bu1 | 172480bf1 | \([0, -1, 0, -3201, 191521]\) | \(-117649/440\) | \(-13570030960640\) | \([]\) | \(290304\) | \(1.2056\) | \(\Gamma_0(N)\)-optimal |
| 172480.bu2 | 172480bf2 | \([0, -1, 0, 28159, -4531295]\) | \(80062991/332750\) | \(-10262335913984000\) | \([]\) | \(870912\) | \(1.7549\) |
Rank
sage: E.rank()
The elliptic curves in class 172480bf have rank \(1\).
Complex multiplication
The elliptic curves in class 172480bf do not have complex multiplication.Modular form 172480.2.a.bf
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.
