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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 481338.ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
481338.ba1 | 481338ba3 | \([1, -1, 0, -3588495147, -82725366978171]\) | \(3957101249824708884951625/772310238681366528\) | \(997413935387729668060741632\) | \([2]\) | \(437944320\) | \(4.1803\) | |
481338.ba2 | 481338ba4 | \([1, -1, 0, -3209348907, -100888670922363]\) | \(-2830680648734534916567625/1766676274677722124288\) | \(-2281605820338523921400588931072\) | \([2]\) | \(875888640\) | \(4.5269\) | |
481338.ba3 | 481338ba1 | \([1, -1, 0, -109254492, 284651829072]\) | \(111675519439697265625/37528570137307392\) | \(48466946254702428674926848\) | \([2]\) | \(145981440\) | \(3.6310\) | \(\Gamma_0(N)\)-optimal* |
481338.ba4 | 481338ba2 | \([1, -1, 0, 318766068, 1967029442208]\) | \(2773679829880629422375/2899504554614368272\) | \(-3744617258254067770457879568\) | \([2]\) | \(291962880\) | \(3.9776\) |
Rank
sage: E.rank()
The elliptic curves in class 481338.ba have rank \(0\).
Complex multiplication
The elliptic curves in class 481338.ba do not have complex multiplication.Modular form 481338.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.