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SageMath
E = EllipticCurve("ci1")
E.isogeny_class()
Elliptic curves in class 19950.ci
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 19950.ci1 | 19950by3 | \([1, 1, 1, -2223438, 1230573531]\) | \(77799851782095807001/3092322318750000\) | \(48317536230468750000\) | \([2]\) | \(589824\) | \(2.5437\) | |
| 19950.ci2 | 19950by2 | \([1, 1, 1, -361438, -57930469]\) | \(334199035754662681/101099003040000\) | \(1579671922500000000\) | \([2, 2]\) | \(294912\) | \(2.1971\) | |
| 19950.ci3 | 19950by1 | \([1, 1, 1, -329438, -72906469]\) | \(253060782505556761/41184460800\) | \(643507200000000\) | \([2]\) | \(147456\) | \(1.8505\) | \(\Gamma_0(N)\)-optimal |
| 19950.ci4 | 19950by4 | \([1, 1, 1, 988562, -387330469]\) | \(6837784281928633319/8113766016106800\) | \(-126777594001668750000\) | \([2]\) | \(589824\) | \(2.5437\) |
Rank
sage: E.rank()
The elliptic curves in class 19950.ci have rank \(1\).
Complex multiplication
The elliptic curves in class 19950.ci do not have complex multiplication.Modular form 19950.2.a.ci
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.
