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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 36300.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 36300.l1 | 36300i1 | \([0, -1, 0, -666508, -209218568]\) | \(-2888047810000/35937\) | \(-407453361004800\) | \([]\) | \(311040\) | \(1.9505\) | \(\Gamma_0(N)\)-optimal |
| 36300.l2 | 36300i2 | \([0, -1, 0, -303508, -435556328]\) | \(-272709010000/7073843073\) | \(-80203164852780499200\) | \([]\) | \(933120\) | \(2.4999\) |
Rank
sage: E.rank()
The elliptic curves in class 36300.l have rank \(1\).
Complex multiplication
The elliptic curves in class 36300.l do not have complex multiplication.Modular form 36300.2.a.l
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
