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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 35904a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35904.z3 | 35904a1 | \([0, -1, 0, -13148673, -18161786367]\) | \(959024269496848362625/11151660319506432\) | \(2923340842796694110208\) | \([2]\) | \(2211840\) | \(2.9314\) | \(\Gamma_0(N)\)-optimal |
| 35904.z4 | 35904a2 | \([0, -1, 0, -2662913, -46341217791]\) | \(-7966267523043306625/3534510366354604032\) | \(-926550685477661319364608\) | \([2]\) | \(4423680\) | \(3.2779\) | |
| 35904.z1 | 35904a3 | \([0, -1, 0, -1062052353, -13321571524095]\) | \(505384091400037554067434625/815656731648\) | \(213819518261133312\) | \([2]\) | \(6635520\) | \(3.4807\) | |
| 35904.z2 | 35904a4 | \([0, -1, 0, -1062042113, -13321841264127]\) | \(-505369473241574671219626625/20303219722982711328\) | \(-5322367231061579878367232\) | \([2]\) | \(13271040\) | \(3.8272\) |
Rank
sage: E.rank()
The elliptic curves in class 35904a have rank \(1\).
Complex multiplication
The elliptic curves in class 35904a do not have complex multiplication.Modular form 35904.2.a.a
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.
