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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 4080l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4080.u3 | 4080l1 | \([0, 1, 0, -951, -9576]\) | \(5951163357184/1129312125\) | \(18068994000\) | \([2]\) | \(3456\) | \(0.68569\) | \(\Gamma_0(N)\)-optimal |
| 4080.u2 | 4080l2 | \([0, 1, 0, -4596, 109980]\) | \(41948679809104/3291890625\) | \(842724000000\) | \([2, 2]\) | \(6912\) | \(1.0323\) | |
| 4080.u1 | 4080l3 | \([0, 1, 0, -72096, 7426980]\) | \(40472803590982276/281883375\) | \(288648576000\) | \([2]\) | \(13824\) | \(1.3788\) | |
| 4080.u4 | 4080l4 | \([0, 1, 0, 4584, 502884]\) | \(10400706415004/112060546875\) | \(-114750000000000\) | \([2]\) | \(13824\) | \(1.3788\) |
Rank
sage: E.rank()
The elliptic curves in class 4080l have rank \(0\).
Complex multiplication
The elliptic curves in class 4080l do not have complex multiplication.Modular form 4080.2.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 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.
