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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 16800.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 16800.c1 | 16800bf3 | \([0, -1, 0, -7938033, 8610947937]\) | \(864335783029582144/59535\) | \(3810240000000\) | \([4]\) | \(368640\) | \(2.3150\) | |
| 16800.c2 | 16800bf2 | \([0, -1, 0, -557408, 99372312]\) | \(2394165105226952/854262178245\) | \(6834097425960000000\) | \([2]\) | \(368640\) | \(2.3150\) | |
| 16800.c3 | 16800bf1 | \([0, -1, 0, -496158, 134652312]\) | \(13507798771700416/3544416225\) | \(3544416225000000\) | \([2, 2]\) | \(184320\) | \(1.9684\) | \(\Gamma_0(N)\)-optimal |
| 16800.c4 | 16800bf4 | \([0, -1, 0, -435408, 168793812]\) | \(-1141100604753992/875529151875\) | \(-7004233215000000000\) | \([2]\) | \(368640\) | \(2.3150\) |
Rank
sage: E.rank()
The elliptic curves in class 16800.c have rank \(0\).
Complex multiplication
The elliptic curves in class 16800.c do not have complex multiplication.Modular form 16800.2.a.c
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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
