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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 17325n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 17325.y1 | 17325n1 | \([0, 0, 1, -20100, -1096844]\) | \(-78843215872/539\) | \(-6139546875\) | \([]\) | \(21600\) | \(1.0590\) | \(\Gamma_0(N)\)-optimal |
| 17325.y2 | 17325n2 | \([0, 0, 1, -11100, -2081219]\) | \(-13278380032/156590819\) | \(-1783667297671875\) | \([]\) | \(64800\) | \(1.6083\) | |
| 17325.y3 | 17325n3 | \([0, 0, 1, 99150, 53870656]\) | \(9463555063808/115539436859\) | \(-1316066397972046875\) | \([]\) | \(194400\) | \(2.1576\) |
Rank
sage: E.rank()
The elliptic curves in class 17325n have rank \(1\).
Complex multiplication
The elliptic curves in class 17325n do not have complex multiplication.Modular form 17325.2.a.n
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.
