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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 6160.i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6160.i1 | 6160p4 | \([0, 0, 0, -52266707, 145440654994]\) | \(3855131356812007128171561/8967612500\) | \(36731340800000\) | \([4]\) | \(245760\) | \(2.7332\) | |
| 6160.i2 | 6160p3 | \([0, 0, 0, -3439187, 2019150866]\) | \(1098325674097093229481/205612182617187500\) | \(842187500000000000000\) | \([2]\) | \(245760\) | \(2.7332\) | |
| 6160.i3 | 6160p2 | \([0, 0, 0, -3266707, 2272454994]\) | \(941226862950447171561/45393906250000\) | \(185933440000000000\) | \([2, 2]\) | \(122880\) | \(2.3866\) | |
| 6160.i4 | 6160p1 | \([0, 0, 0, -193427, 39409746]\) | \(-195395722614328041/50730248800000\) | \(-207791099084800000\) | \([2]\) | \(61440\) | \(2.0400\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6160.i have rank \(1\).
Complex multiplication
The elliptic curves in class 6160.i do not have complex multiplication.Modular form 6160.2.a.i
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
