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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 21780.bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 21780.bb1 | 21780p2 | \([0, 0, 0, -475167, 100817926]\) | \(26962544/5625\) | \(2475279168104160000\) | \([2]\) | \(405504\) | \(2.2444\) | |
| 21780.bb2 | 21780p1 | \([0, 0, 0, 63888, 9502009]\) | \(1048576/2025\) | \(-55693781282343600\) | \([2]\) | \(202752\) | \(1.8978\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 21780.bb have rank \(0\).
Complex multiplication
The elliptic curves in class 21780.bb do not have complex multiplication.Modular form 21780.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
