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SageMath
E = EllipticCurve("cm1")
E.isogeny_class()
Elliptic curves in class 33600.cm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 33600.cm1 | 33600ca2 | \([0, -1, 0, -22433, -1360863]\) | \(-7620530425/526848\) | \(-86318776320000\) | \([]\) | \(124416\) | \(1.4250\) | |
| 33600.cm2 | 33600ca1 | \([0, -1, 0, 1567, -2463]\) | \(2595575/1512\) | \(-247726080000\) | \([]\) | \(41472\) | \(0.87573\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 33600.cm have rank \(1\).
Complex multiplication
The elliptic curves in class 33600.cm do not have complex multiplication.Modular form 33600.2.a.cm
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.
