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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 234416bi
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 234416.bi1 | 234416bi1 | \([0, 1, 0, -9277, 808471]\) | \(-2932006912/7750379\) | \(-233427030776576\) | \([]\) | \(663552\) | \(1.4445\) | \(\Gamma_0(N)\)-optimal |
| 234416.bi2 | 234416bi2 | \([0, 1, 0, 80883, -18305449]\) | \(1942951190528/5944921619\) | \(-179050005389755136\) | \([]\) | \(1990656\) | \(1.9938\) |
Rank
sage: E.rank()
The elliptic curves in class 234416bi have rank \(1\).
Complex multiplication
The elliptic curves in class 234416bi do not have complex multiplication.Modular form 234416.2.a.bi
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.
