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SageMath
E = EllipticCurve("bp1")
E.isogeny_class()
Elliptic curves in class 69360.bp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 69360.bp1 | 69360q4 | \([0, -1, 0, -20835840, 36613767600]\) | \(40472803590982276/281883375\) | \(6967274919951744000\) | \([2]\) | \(3981312\) | \(2.7954\) | |
| 69360.bp2 | 69360q2 | \([0, -1, 0, -1328340, 548301600]\) | \(41948679809104/3291890625\) | \(20341308697956000000\) | \([2, 2]\) | \(1990656\) | \(2.4489\) | |
| 69360.bp3 | 69360q1 | \([0, -1, 0, -274935, -45397458]\) | \(5951163357184/1129312125\) | \(436141589435586000\) | \([2]\) | \(995328\) | \(2.1023\) | \(\Gamma_0(N)\)-optimal |
| 69360.bp4 | 69360q3 | \([0, -1, 0, 1324680, 2462720832]\) | \(10400706415004/112060546875\) | \(-2769786042750000000000\) | \([4]\) | \(3981312\) | \(2.7954\) |
Rank
sage: E.rank()
The elliptic curves in class 69360.bp have rank \(0\).
Complex multiplication
The elliptic curves in class 69360.bp do not have complex multiplication.Modular form 69360.2.a.bp
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
