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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 28050n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 28050.l3 | 28050n1 | \([1, 1, 0, -5136200, -4437240000]\) | \(959024269496848362625/11151660319506432\) | \(174244692492288000000\) | \([2]\) | \(1658880\) | \(2.6964\) | \(\Gamma_0(N)\)-optimal |
| 28050.l4 | 28050n2 | \([1, 1, 0, -1040200, -11314424000]\) | \(-7966267523043306625/3534510366354604032\) | \(-55226724474290688000000\) | \([2]\) | \(3317760\) | \(3.0429\) | |
| 28050.l1 | 28050n3 | \([1, 1, 0, -414864200, -3252596088000]\) | \(505384091400037554067434625/815656731648\) | \(12744636432000000\) | \([2]\) | \(4976640\) | \(3.2457\) | |
| 28050.l2 | 28050n4 | \([1, 1, 0, -414860200, -3252661940000]\) | \(-505369473241574671219626625/20303219722982711328\) | \(-317237808171604864500000\) | \([2]\) | \(9953280\) | \(3.5922\) |
Rank
sage: E.rank()
The elliptic curves in class 28050n have rank \(1\).
Complex multiplication
The elliptic curves in class 28050n do not have complex multiplication.Modular form 28050.2.a.n
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
