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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 14450g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 14450.a4 | 14450g1 | \([1, 0, 1, -21826, 766548]\) | \(3048625/1088\) | \(410338673000000\) | \([2]\) | \(82944\) | \(1.5049\) | \(\Gamma_0(N)\)-optimal |
| 14450.a3 | 14450g2 | \([1, 0, 1, -310826, 66658548]\) | \(8805624625/2312\) | \(871969680125000\) | \([2]\) | \(165888\) | \(1.8515\) | |
| 14450.a2 | 14450g3 | \([1, 0, 1, -744326, -247195452]\) | \(120920208625/19652\) | \(7411742281062500\) | \([2]\) | \(248832\) | \(2.0542\) | |
| 14450.a1 | 14450g4 | \([1, 0, 1, -816576, -196331452]\) | \(159661140625/48275138\) | \(18206944913430031250\) | \([2]\) | \(497664\) | \(2.4008\) |
Rank
sage: E.rank()
The elliptic curves in class 14450g have rank \(1\).
Complex multiplication
The elliptic curves in class 14450g do not have complex multiplication.Modular form 14450.2.a.g
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
