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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 6960.w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6960.w1 | 6960be3 | \([0, -1, 0, -111360, 14340672]\) | \(37286818682653441/1305\) | \(5345280\) | \([4]\) | \(20480\) | \(1.2373\) | |
| 6960.w2 | 6960be2 | \([0, -1, 0, -6960, 225792]\) | \(9104453457841/1703025\) | \(6975590400\) | \([2, 2]\) | \(10240\) | \(0.89069\) | |
| 6960.w3 | 6960be4 | \([0, -1, 0, -6240, 273600]\) | \(-6561258219361/3978455625\) | \(-16295754240000\) | \([4]\) | \(20480\) | \(1.2373\) | |
| 6960.w4 | 6960be1 | \([0, -1, 0, -480, 2880]\) | \(2992209121/951345\) | \(3896709120\) | \([2]\) | \(5120\) | \(0.54412\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6960.w have rank \(0\).
Complex multiplication
The elliptic curves in class 6960.w do not have complex multiplication.Modular form 6960.2.a.w
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
