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SageMath
E = EllipticCurve("lb1")
E.isogeny_class()
Elliptic curves in class 352800lb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 352800.lb1 | 352800lb1 | \([0, 0, 0, -6825, -196000]\) | \(140608/15\) | \(3750705000000\) | \([2]\) | \(491520\) | \(1.1471\) | \(\Gamma_0(N)\)-optimal |
| 352800.lb2 | 352800lb2 | \([0, 0, 0, 8925, -967750]\) | \(39304/225\) | \(-450084600000000\) | \([2]\) | \(983040\) | \(1.4937\) |
Rank
sage: E.rank()
The elliptic curves in class 352800lb have rank \(1\).
Complex multiplication
The elliptic curves in class 352800lb do not have complex multiplication.Modular form 352800.2.a.lb
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
