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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 296208ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 296208.ba2 | 296208ba1 | \([0, 0, 0, -7174977051, 224847845301706]\) | \(7722211175253055152433/340131399900069888\) | \(1799245038477598970730157965312\) | \([2]\) | \(373800960\) | \(4.5685\) | \(\Gamma_0(N)\)-optimal |
| 296208.ba1 | 296208ba2 | \([0, 0, 0, -19307656731, -736087077249590]\) | \(150476552140919246594353/42832838728685592576\) | \(226579411924746749065986859597824\) | \([2]\) | \(747601920\) | \(4.9151\) |
Rank
sage: E.rank()
The elliptic curves in class 296208ba have rank \(1\).
Complex multiplication
The elliptic curves in class 296208ba do not have complex multiplication.Modular form 296208.2.a.ba
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
