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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 48510x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 48510.q3 | 48510x1 | \([1, -1, 0, -220950, -34655580]\) | \(13908844989649/1980372240\) | \(169848845160881040\) | \([2]\) | \(589824\) | \(2.0319\) | \(\Gamma_0(N)\)-optimal |
| 48510.q2 | 48510x2 | \([1, -1, 0, -935370, 313838496]\) | \(1055257664218129/115307784900\) | \(9889501431975372900\) | \([2, 2]\) | \(1179648\) | \(2.3785\) | |
| 48510.q4 | 48510x3 | \([1, -1, 0, 1247580, 1559429766]\) | \(2503876820718671/13702874328990\) | \(-1175242377747950147790\) | \([2]\) | \(2359296\) | \(2.7250\) | |
| 48510.q1 | 48510x4 | \([1, -1, 0, -14549040, 21363295050]\) | \(3971101377248209009/56495958750\) | \(4845439234163508750\) | \([2]\) | \(2359296\) | \(2.7250\) |
Rank
sage: E.rank()
The elliptic curves in class 48510x have rank \(0\).
Complex multiplication
The elliptic curves in class 48510x do not have complex multiplication.Modular form 48510.2.a.x
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.
