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SageMath
E = EllipticCurve("hb1")
E.isogeny_class()
Elliptic curves in class 152880hb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 152880.ct4 | 152880hb1 | \([0, -1, 0, 476705, 137534650]\) | \(6364491337435136/8034291412875\) | \(-15123621606933294000\) | \([2]\) | \(4423680\) | \(2.3662\) | \(\Gamma_0(N)\)-optimal |
| 152880.ct3 | 152880hb2 | \([0, -1, 0, -2877100, 1332830752]\) | \(87450143958975184/25164018140625\) | \(757893521977956000000\) | \([2, 2]\) | \(8847360\) | \(2.7128\) | |
| 152880.ct1 | 152880hb3 | \([0, -1, 0, -42205480, 105537306400]\) | \(69014771940559650916/9797607421875\) | \(1180343004750000000000\) | \([4]\) | \(17694720\) | \(3.0594\) | |
| 152880.ct2 | 152880hb4 | \([0, -1, 0, -17209600, -26426355248]\) | \(4678944235881273796/202428825314625\) | \(24387122042306884224000\) | \([2]\) | \(17694720\) | \(3.0594\) |
Rank
sage: E.rank()
The elliptic curves in class 152880hb have rank \(0\).
Complex multiplication
The elliptic curves in class 152880hb do not have complex multiplication.Modular form 152880.2.a.hb
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.
