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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 17745n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 17745.f3 | 17745n1 | \([1, 0, 0, -426, 3171]\) | \(1771561/105\) | \(506814945\) | \([2]\) | \(7680\) | \(0.42337\) | \(\Gamma_0(N)\)-optimal |
| 17745.f2 | 17745n2 | \([1, 0, 0, -1271, -13560]\) | \(47045881/11025\) | \(53215569225\) | \([2, 2]\) | \(15360\) | \(0.76994\) | |
| 17745.f1 | 17745n3 | \([1, 0, 0, -19016, -1010829]\) | \(157551496201/13125\) | \(63351868125\) | \([2]\) | \(30720\) | \(1.1165\) | |
| 17745.f4 | 17745n4 | \([1, 0, 0, 2954, -83695]\) | \(590589719/972405\) | \(-4693613205645\) | \([2]\) | \(30720\) | \(1.1165\) |
Rank
sage: E.rank()
The elliptic curves in class 17745n have rank \(0\).
Complex multiplication
The elliptic curves in class 17745n do not have complex multiplication.Modular form 17745.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
