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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 19074n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 19074.q3 | 19074n1 | \([1, 1, 1, -59374478, -174341906485]\) | \(959024269496848362625/11151660319506432\) | \(269173970426648548343808\) | \([2]\) | \(3317760\) | \(3.3082\) | \(\Gamma_0(N)\)-optimal |
| 19074.q4 | 19074n2 | \([1, 1, 1, -12024718, -444690096181]\) | \(-7966267523043306625/3534510366354604032\) | \(-85314487849099533290078208\) | \([2]\) | \(6635520\) | \(3.6548\) | |
| 19074.q1 | 19074n3 | \([1, 1, 1, -4795830158, -127835240812597]\) | \(505384091400037554067434625/815656731648\) | \(19687970640468083712\) | \([2]\) | \(9953280\) | \(3.8576\) | |
| 19074.q2 | 19074n4 | \([1, 1, 1, -4795783918, -127837829105845]\) | \(-505369473241574671219626625/20303219722982711328\) | \(-490070366985656080486681632\) | \([2]\) | \(19906560\) | \(4.2041\) |
Rank
sage: E.rank()
The elliptic curves in class 19074n have rank \(0\).
Complex multiplication
The elliptic curves in class 19074n do not have complex multiplication.Modular form 19074.2.a.n
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
