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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 143143v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 143143.v1 | 143143v1 | \([0, 1, 1, -1826777, -950949125]\) | \(-78843215872/539\) | \(-4608981765999611\) | \([]\) | \(1728000\) | \(2.1864\) | \(\Gamma_0(N)\)-optimal |
| 143143.v2 | 143143v2 | \([0, 1, 1, -1008817, -1803570180]\) | \(-13278380032/156590819\) | \(-1339005991639972987331\) | \([]\) | \(5184000\) | \(2.7357\) | |
| 143143.v3 | 143143v3 | \([0, 1, 1, 9011193, 46678248205]\) | \(9463555063808/115539436859\) | \(-987976173909080460395291\) | \([]\) | \(15552000\) | \(3.2850\) |
Rank
sage: E.rank()
The elliptic curves in class 143143v have rank \(1\).
Complex multiplication
The elliptic curves in class 143143v do not have complex multiplication.Modular form 143143.2.a.v
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
