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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 199962bl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 199962.f2 | 199962bl1 | \([1, -1, 0, -6447, -253515]\) | \(-7414875/2744\) | \(-10967682944232\) | \([]\) | \(392040\) | \(1.2123\) | \(\Gamma_0(N)\)-optimal |
| 199962.f3 | 199962bl2 | \([1, -1, 0, 49098, 2564468]\) | \(4492125/3584\) | \(-10443024805022208\) | \([]\) | \(1176120\) | \(1.7616\) | |
| 199962.f1 | 199962bl3 | \([1, -1, 0, -561897, -161978337]\) | \(-545407363875/14\) | \(-503618094378\) | \([]\) | \(1176120\) | \(1.7616\) |
Rank
sage: E.rank()
The elliptic curves in class 199962bl have rank \(0\).
Complex multiplication
The elliptic curves in class 199962bl do not have complex multiplication.Modular form 199962.2.a.bl
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.
\(\left(\begin{array}{rrr} 1 & 3 & 3 \\ 3 & 1 & 9 \\ 3 & 9 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
