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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 2070n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2070.m3 | 2070n1 | \([1, -1, 1, -113, -223]\) | \(217081801/88320\) | \(64385280\) | \([2]\) | \(512\) | \(0.19608\) | \(\Gamma_0(N)\)-optimal |
| 2070.m2 | 2070n2 | \([1, -1, 1, -833, 9281]\) | \(87587538121/1904400\) | \(1388307600\) | \([2, 2]\) | \(1024\) | \(0.54266\) | |
| 2070.m1 | 2070n3 | \([1, -1, 1, -13253, 590537]\) | \(353108405631241/172500\) | \(125752500\) | \([2]\) | \(2048\) | \(0.88923\) | |
| 2070.m4 | 2070n4 | \([1, -1, 1, 67, 27641]\) | \(46268279/453342420\) | \(-330486624180\) | \([2]\) | \(2048\) | \(0.88923\) |
Rank
sage: E.rank()
The elliptic curves in class 2070n have rank \(1\).
Complex multiplication
The elliptic curves in class 2070n do not have complex multiplication.Modular form 2070.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
