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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 59150l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 59150.o2 | 59150l1 | \([1, 1, 0, 27375, 11465875]\) | \(30080231/768950\) | \(-57993355946093750\) | \([]\) | \(580608\) | \(1.8967\) | \(\Gamma_0(N)\)-optimal |
| 59150.o1 | 59150l2 | \([1, 1, 0, -247250, -315612500]\) | \(-22164361129/557375000\) | \(-42036604162109375000\) | \([]\) | \(1741824\) | \(2.4461\) |
Rank
sage: E.rank()
The elliptic curves in class 59150l have rank \(0\).
Complex multiplication
The elliptic curves in class 59150l do not have complex multiplication.Modular form 59150.2.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 Cremona 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 Cremona labels.
