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SageMath
E = EllipticCurve("gi1")
E.isogeny_class()
Elliptic curves in class 162240gi
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 162240.fl3 | 162240gi1 | \([0, 1, 0, -43996, 3537314]\) | \(30488290624/195\) | \(60238576320\) | \([2]\) | \(258048\) | \(1.2531\) | \(\Gamma_0(N)\)-optimal |
| 162240.fl2 | 162240gi2 | \([0, 1, 0, -44841, 3393495]\) | \(504358336/38025\) | \(751777432473600\) | \([2, 2]\) | \(516096\) | \(1.5997\) | |
| 162240.fl4 | 162240gi3 | \([0, 1, 0, 43039, 15151839]\) | \(55742968/658125\) | \(-104092259880960000\) | \([2]\) | \(1032192\) | \(1.9463\) | |
| 162240.fl1 | 162240gi4 | \([0, 1, 0, -146241, -17555745]\) | \(2186875592/428415\) | \(67760205913620480\) | \([2]\) | \(1032192\) | \(1.9463\) |
Rank
sage: E.rank()
The elliptic curves in class 162240gi have rank \(0\).
Complex multiplication
The elliptic curves in class 162240gi do not have complex multiplication.Modular form 162240.2.a.gi
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.
