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SageMath
E = EllipticCurve("qq1")
E.isogeny_class()
Elliptic curves in class 235200qq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 235200.qq4 | 235200qq1 | \([0, 1, 0, -1416508, 977960738]\) | \(-2671731885376/1969120125\) | \(-231665013586125000000\) | \([2]\) | \(7077888\) | \(2.6071\) | \(\Gamma_0(N)\)-optimal |
| 235200.qq3 | 235200qq2 | \([0, 1, 0, -25726633, 50205963863]\) | \(250094631024064/62015625\) | \(466948881000000000000\) | \([2, 2]\) | \(14155776\) | \(2.9536\) | |
| 235200.qq1 | 235200qq3 | \([0, 1, 0, -411601633, 3213995088863]\) | \(128025588102048008/7875\) | \(474360768000000000\) | \([2]\) | \(28311552\) | \(3.3002\) | |
| 235200.qq2 | 235200qq4 | \([0, 1, 0, -28813633, 37398000863]\) | \(43919722445768/15380859375\) | \(926485875000000000000000\) | \([2]\) | \(28311552\) | \(3.3002\) |
Rank
sage: E.rank()
The elliptic curves in class 235200qq have rank \(1\).
Complex multiplication
The elliptic curves in class 235200qq do not have complex multiplication.Modular form 235200.2.a.qq
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.
