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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 100800.bl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 100800.bl1 | 100800jj1 | \([0, 0, 0, -24300, -702000]\) | \(78732/35\) | \(705438720000000\) | \([2]\) | \(442368\) | \(1.5447\) | \(\Gamma_0(N)\)-optimal |
| 100800.bl2 | 100800jj2 | \([0, 0, 0, 83700, -5238000]\) | \(1608714/1225\) | \(-49380710400000000\) | \([2]\) | \(884736\) | \(1.8913\) |
Rank
sage: E.rank()
The elliptic curves in class 100800.bl have rank \(2\).
Complex multiplication
The elliptic curves in class 100800.bl do not have complex multiplication.Modular form 100800.2.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 LMFDB 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 LMFDB labels.
