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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 308898ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
308898.ba1 | 308898ba1 | \([1, -1, 1, -10969097, -13911184695]\) | \(39616946929/226368\) | \(834008229559914426432\) | \([2]\) | \(39536640\) | \(2.8559\) | \(\Gamma_0(N)\)-optimal |
308898.ba2 | 308898ba2 | \([1, -1, 1, -4791137, -29491999815]\) | \(-3301293169/100082952\) | \(-368735888494177165786248\) | \([2]\) | \(79073280\) | \(3.2024\) |
Rank
sage: E.rank()
The elliptic curves in class 308898ba have rank \(0\).
Complex multiplication
The elliptic curves in class 308898ba do not have complex multiplication.Modular form 308898.2.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.