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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 16800f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 16800.a3 | 16800f1 | \([0, -1, 0, -131258, 18343512]\) | \(250094631024064/62015625\) | \(62015625000000\) | \([2, 2]\) | \(73728\) | \(1.6341\) | \(\Gamma_0(N)\)-optimal |
| 16800.a2 | 16800f2 | \([0, -1, 0, -147008, 13681512]\) | \(43919722445768/15380859375\) | \(123046875000000000\) | \([2]\) | \(147456\) | \(1.9807\) | |
| 16800.a1 | 16800f3 | \([0, -1, 0, -2100008, 1172031012]\) | \(128025588102048008/7875\) | \(63000000000\) | \([4]\) | \(147456\) | \(1.9807\) | |
| 16800.a4 | 16800f4 | \([0, -1, 0, -115633, 22859137]\) | \(-2671731885376/1969120125\) | \(-126023688000000000\) | \([2]\) | \(147456\) | \(1.9807\) |
Rank
sage: E.rank()
The elliptic curves in class 16800f have rank \(1\).
Complex multiplication
The elliptic curves in class 16800f do not have complex multiplication.Modular form 16800.2.a.f
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
