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SageMath
E = EllipticCurve("ee1")
E.isogeny_class()
Elliptic curves in class 73920ee
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
73920.f3 | 73920ee1 | \([0, -1, 0, -316, 2266]\) | \(54698902336/144375\) | \(9240000\) | \([2]\) | \(20480\) | \(0.21150\) | \(\Gamma_0(N)\)-optimal |
73920.f2 | 73920ee2 | \([0, -1, 0, -441, 441]\) | \(2320940224/1334025\) | \(5464166400\) | \([2, 2]\) | \(40960\) | \(0.55808\) | |
73920.f4 | 73920ee3 | \([0, -1, 0, 1759, 1761]\) | \(18357958072/10696455\) | \(-350501437440\) | \([2]\) | \(81920\) | \(0.90465\) | |
73920.f1 | 73920ee4 | \([0, -1, 0, -4641, -119679]\) | \(337444269128/1537305\) | \(50374410240\) | \([2]\) | \(81920\) | \(0.90465\) |
Rank
sage: E.rank()
The elliptic curves in class 73920ee have rank \(2\).
Complex multiplication
The elliptic curves in class 73920ee do not have complex multiplication.Modular form 73920.2.a.ee
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.