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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 81120.bq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 81120.bq1 | 81120cc4 | \([0, 1, 0, -212320, -37721332]\) | \(428320044872/73125\) | \(180715728960000\) | \([2]\) | \(516096\) | \(1.7422\) | |
| 81120.bq2 | 81120cc3 | \([0, 1, 0, -90640, 10117160]\) | \(33324076232/1285245\) | \(3176259652200960\) | \([2]\) | \(516096\) | \(1.7422\) | |
| 81120.bq3 | 81120cc1 | \([0, 1, 0, -14590, -469000]\) | \(1111934656/342225\) | \(105718701441600\) | \([2, 2]\) | \(258048\) | \(1.3956\) | \(\Gamma_0(N)\)-optimal |
| 81120.bq4 | 81120cc2 | \([0, 1, 0, 40335, -3116385]\) | \(367061696/426465\) | \(-8431473050357760\) | \([4]\) | \(516096\) | \(1.7422\) |
Rank
sage: E.rank()
The elliptic curves in class 81120.bq have rank \(0\).
Complex multiplication
The elliptic curves in class 81120.bq do not have complex multiplication.Modular form 81120.2.a.bq
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.
