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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 6960.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6960.l1 | 6960bf3 | \([0, -1, 0, -4120, 101680]\) | \(1888690601881/31827645\) | \(130366033920\) | \([4]\) | \(12288\) | \(0.93080\) | |
| 6960.l2 | 6960bf2 | \([0, -1, 0, -520, -2000]\) | \(3803721481/1703025\) | \(6975590400\) | \([2, 2]\) | \(6144\) | \(0.58422\) | |
| 6960.l3 | 6960bf1 | \([0, -1, 0, -440, -3408]\) | \(2305199161/1305\) | \(5345280\) | \([2]\) | \(3072\) | \(0.23765\) | \(\Gamma_0(N)\)-optimal |
| 6960.l4 | 6960bf4 | \([0, -1, 0, 1800, -16848]\) | \(157376536199/118918125\) | \(-487088640000\) | \([2]\) | \(12288\) | \(0.93080\) |
Rank
sage: E.rank()
The elliptic curves in class 6960.l have rank \(0\).
Complex multiplication
The elliptic curves in class 6960.l do not have complex multiplication.Modular form 6960.2.a.l
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.
