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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 10192.bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 10192.bb1 | 10192r3 | \([0, 1, 0, -12279808, -16566959564]\) | \(-424962187484640625/182\) | \(-87704035328\) | \([]\) | \(124416\) | \(2.3466\) | |
| 10192.bb2 | 10192r2 | \([0, 1, 0, -151328, -22856716]\) | \(-795309684625/6028568\) | \(-2905108466204672\) | \([]\) | \(41472\) | \(1.7973\) | |
| 10192.bb3 | 10192r1 | \([0, 1, 0, 5472, -164620]\) | \(37595375/46592\) | \(-22452233043968\) | \([]\) | \(13824\) | \(1.2479\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 10192.bb have rank \(1\).
Complex multiplication
The elliptic curves in class 10192.bb do not have complex multiplication.Modular form 10192.2.a.bb
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
