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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 152460bf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 152460.bp1 | 152460bf1 | \([0, 0, 0, -37426752, 88129491021]\) | \(10392086293512192/1684375\) | \(939736667642850000\) | \([2]\) | \(8985600\) | \(2.8506\) | \(\Gamma_0(N)\)-optimal |
| 152460.bp2 | 152460bf2 | \([0, 0, 0, -37312407, 88694744094]\) | \(-643570518871152/8271484375\) | \(-73836452457652500000000\) | \([2]\) | \(17971200\) | \(3.1972\) |
Rank
sage: E.rank()
The elliptic curves in class 152460bf have rank \(1\).
Complex multiplication
The elliptic curves in class 152460bf do not have complex multiplication.Modular form 152460.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
