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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 369600.ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 369600.ba1 | 369600ba2 | \([0, -1, 0, -8398593, -9365438943]\) | \(7997484869919944276/116700507\) | \(956010553344000\) | \([2]\) | \(9142272\) | \(2.4263\) | |
| 369600.ba2 | 369600ba1 | \([0, -1, 0, -525393, -145921743]\) | \(7831544736466064/29831377653\) | \(61094661433344000\) | \([2]\) | \(4571136\) | \(2.0797\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 369600.ba have rank \(1\).
Complex multiplication
The elliptic curves in class 369600.ba do not have complex multiplication.Modular form 369600.2.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 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.
