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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 61770.be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 61770.be1 | 61770bi4 | \([1, 0, 0, -1849562890, -26210282651680]\) | \(699730849413758307773625675219361/108165432519805493533336117380\) | \(108165432519805493533336117380\) | \([2]\) | \(71680000\) | \(4.2945\) | |
| 61770.be2 | 61770bi2 | \([1, 0, 0, -494845990, 4236906928100]\) | \(13400897273900477255187118481761/1631134479352924800000\) | \(1631134479352924800000\) | \([10]\) | \(14336000\) | \(3.4898\) | |
| 61770.be3 | 61770bi1 | \([1, 0, 0, -30845990, 66567728100]\) | \(-3245785780942463481262481761/36104958351360000000000\) | \(-36104958351360000000000\) | \([10]\) | \(7168000\) | \(3.1432\) | \(\Gamma_0(N)\)-optimal |
| 61770.be4 | 61770bi3 | \([1, 0, 0, 201552010, -2261054856300]\) | \(905493032039962326335212110239/2732588418593618058238383600\) | \(-2732588418593618058238383600\) | \([2]\) | \(35840000\) | \(3.9479\) |
Rank
sage: E.rank()
The elliptic curves in class 61770.be have rank \(1\).
Complex multiplication
The elliptic curves in class 61770.be do not have complex multiplication.Modular form 61770.2.a.be
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.
\(\left(\begin{array}{rrrr} 1 & 5 & 10 & 2 \\ 5 & 1 & 2 & 10 \\ 10 & 2 & 1 & 5 \\ 2 & 10 & 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
