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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 18150.z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 18150.z1 | 18150bj3 | \([1, 0, 1, -4847626, -4108476352]\) | \(455129268177961/4392300\) | \(121581677817187500\) | \([2]\) | \(737280\) | \(2.4397\) | |
| 18150.z2 | 18150bj2 | \([1, 0, 1, -310126, -61026352]\) | \(119168121961/10890000\) | \(301442176406250000\) | \([2, 2]\) | \(368640\) | \(2.0931\) | |
| 18150.z3 | 18150bj1 | \([1, 0, 1, -68126, 5765648]\) | \(1263214441/211200\) | \(5846151300000000\) | \([2]\) | \(184320\) | \(1.7465\) | \(\Gamma_0(N)\)-optimal |
| 18150.z4 | 18150bj4 | \([1, 0, 1, 355374, -287296352]\) | \(179310732119/1392187500\) | \(-38536641870117187500\) | \([2]\) | \(737280\) | \(2.4397\) |
Rank
sage: E.rank()
The elliptic curves in class 18150.z have rank \(1\).
Complex multiplication
The elliptic curves in class 18150.z do not have complex multiplication.Modular form 18150.2.a.z
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
