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SageMath
sage: E = EllipticCurve("75150.x1")
sage: E.isogeny_class()
Elliptic curves in class 75150.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 75150.x1 | 75150q2 | [1, -1, 0, -4759542, -3835054634] | [2] | 4128768 | |
| 75150.x2 | 75150q1 | [1, -1, 0, 161208, -228144884] | [2] | 2064384 | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 75150.x have rank \(1\).
Modular form 75150.2.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 LMFDB 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 LMFDB labels.
