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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 2670d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2670.d4 | 2670d1 | \([1, 1, 1, -850, -9265]\) | \(67922306042401/5006250000\) | \(5006250000\) | \([4]\) | \(2048\) | \(0.60711\) | \(\Gamma_0(N)\)-optimal |
| 2670.d2 | 2670d2 | \([1, 1, 1, -13350, -599265]\) | \(263129501187842401/1604002500\) | \(1604002500\) | \([2, 2]\) | \(4096\) | \(0.95368\) | |
| 2670.d1 | 2670d3 | \([1, 1, 1, -213600, -38086065]\) | \(1077773706461706278401/40050\) | \(40050\) | \([2]\) | \(8192\) | \(1.3003\) | |
| 2670.d3 | 2670d4 | \([1, 1, 1, -13100, -622465]\) | \(-248622066042206401/20582592160050\) | \(-20582592160050\) | \([2]\) | \(8192\) | \(1.3003\) |
Rank
sage: E.rank()
The elliptic curves in class 2670d have rank \(0\).
Complex multiplication
The elliptic curves in class 2670d do not have complex multiplication.Modular form 2670.2.a.d
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.
