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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 86394.ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
86394.ba1 | 86394be2 | \([1, 0, 1, -2681581312, 53441474067980]\) | \(904403962624187353472747/130919442993517374\) | \(308701198313570419991683434\) | \([2]\) | \(60217344\) | \(4.0979\) | |
86394.ba2 | 86394be1 | \([1, 0, 1, -2681488142, 53445373791500]\) | \(904309696913292313535627/18953705484\) | \(44691846081891837444\) | \([2]\) | \(30108672\) | \(3.7513\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 86394.ba have rank \(1\).
Complex multiplication
The elliptic curves in class 86394.ba do not have complex multiplication.Modular form 86394.2.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.