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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 479808bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 479808.bb2 | 479808bb1 | \([0, 0, 0, -4704, -779296]\) | \(-221184/4913\) | \(-255692922863616\) | \([]\) | \(1658880\) | \(1.4454\) | \(\Gamma_0(N)\)-optimal |
| 479808.bb1 | 479808bb2 | \([0, 0, 0, -804384, -277681824]\) | \(-1517101056/17\) | \(-644983186046976\) | \([]\) | \(4976640\) | \(1.9947\) |
Rank
sage: E.rank()
The elliptic curves in class 479808bb have rank \(1\).
Complex multiplication
The elliptic curves in class 479808bb do not have complex multiplication.Modular form 479808.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
