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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 33930.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 33930.m1 | 33930q1 | \([1, -1, 0, -87219, 3260533]\) | \(100654290922421809/52033093632000\) | \(37932125257728000\) | \([2]\) | \(307200\) | \(1.8733\) | \(\Gamma_0(N)\)-optimal |
| 33930.m2 | 33930q2 | \([1, -1, 0, 327501, 25074805]\) | \(5328847957372469711/3458851344000000\) | \(-2521502629776000000\) | \([2]\) | \(614400\) | \(2.2198\) |
Rank
sage: E.rank()
The elliptic curves in class 33930.m have rank \(1\).
Complex multiplication
The elliptic curves in class 33930.m do not have complex multiplication.Modular form 33930.2.a.m
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.
