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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 155682i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 155682.v3 | 155682i1 | \([1, -1, 1, -4505, -120831]\) | \(-140625/8\) | \(-575102385288\) | \([]\) | \(181440\) | \(1.0134\) | \(\Gamma_0(N)\)-optimal |
| 155682.v4 | 155682i2 | \([1, -1, 1, 24325, -232307]\) | \(3375/2\) | \(-943311687468642\) | \([]\) | \(544320\) | \(1.5627\) | |
| 155682.v2 | 155682i3 | \([1, -1, 1, -90995, 21484371]\) | \(-1159088625/2097152\) | \(-150759639688937472\) | \([]\) | \(1270080\) | \(1.9864\) | |
| 155682.v1 | 155682i4 | \([1, -1, 1, -9316595, 10947792979]\) | \(-189613868625/128\) | \(-60371947997993088\) | \([]\) | \(3810240\) | \(2.5357\) |
Rank
sage: E.rank()
The elliptic curves in class 155682i have rank \(1\).
Complex multiplication
The elliptic curves in class 155682i do not have complex multiplication.Modular form 155682.2.a.i
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 7 & 21 \\ 3 & 1 & 21 & 7 \\ 7 & 21 & 1 & 3 \\ 21 & 7 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
