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SageMath
E = EllipticCurve("cx1")
E.isogeny_class()
Elliptic curves in class 42350.cx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 42350.cx1 | 42350cq4 | \([1, 1, 1, -79000963, 262577985781]\) | \(1969902499564819009/63690429687500\) | \(1762991895431518554687500\) | \([2]\) | \(9953280\) | \(3.4263\) | |
| 42350.cx2 | 42350cq2 | \([1, 1, 1, -10817463, -13577047219]\) | \(5057359576472449/51765560000\) | \(1432903863111875000000\) | \([2]\) | \(3317760\) | \(2.8770\) | |
| 42350.cx3 | 42350cq1 | \([1, 1, 1, -169463, -522599219]\) | \(-19443408769/4249907200\) | \(-117640153892800000000\) | \([2]\) | \(1658880\) | \(2.5304\) | \(\Gamma_0(N)\)-optimal |
| 42350.cx4 | 42350cq3 | \([1, 1, 1, 1524537, 14076292781]\) | \(14156681599871/3100231750000\) | \(-85816400925964843750000\) | \([2]\) | \(4976640\) | \(3.0798\) |
Rank
sage: E.rank()
The elliptic curves in class 42350.cx have rank \(0\).
Complex multiplication
The elliptic curves in class 42350.cx do not have complex multiplication.Modular form 42350.2.a.cx
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
