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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 1680.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1680.l1 | 1680f3 | \([0, 1, 0, -456, -3900]\) | \(10262905636/13125\) | \(13440000\) | \([2]\) | \(512\) | \(0.27571\) | |
| 1680.l2 | 1680f4 | \([0, 1, 0, -336, 2244]\) | \(4108974916/36015\) | \(36879360\) | \([2]\) | \(512\) | \(0.27571\) | |
| 1680.l3 | 1680f2 | \([0, 1, 0, -36, -36]\) | \(20720464/11025\) | \(2822400\) | \([2, 2]\) | \(256\) | \(-0.070861\) | |
| 1680.l4 | 1680f1 | \([0, 1, 0, 9, 0]\) | \(4499456/2835\) | \(-45360\) | \([2]\) | \(128\) | \(-0.41743\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1680.l have rank \(0\).
Complex multiplication
The elliptic curves in class 1680.l do not have complex multiplication.Modular form 1680.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
