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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 4368.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4368.d1 | 4368t3 | \([0, -1, 0, -31304, -2120976]\) | \(828279937799497/193444524\) | \(792348770304\) | \([2]\) | \(9216\) | \(1.2738\) | |
| 4368.d2 | 4368t2 | \([0, -1, 0, -2184, -24336]\) | \(281397674377/96589584\) | \(395630936064\) | \([2, 2]\) | \(4608\) | \(0.92722\) | |
| 4368.d3 | 4368t1 | \([0, -1, 0, -904, 10480]\) | \(19968681097/628992\) | \(2576351232\) | \([2]\) | \(2304\) | \(0.58064\) | \(\Gamma_0(N)\)-optimal |
| 4368.d4 | 4368t4 | \([0, -1, 0, 6456, -176400]\) | \(7264187703863/7406095788\) | \(-30335368347648\) | \([4]\) | \(9216\) | \(1.2738\) |
Rank
sage: E.rank()
The elliptic curves in class 4368.d have rank \(0\).
Complex multiplication
The elliptic curves in class 4368.d do not have complex multiplication.Modular form 4368.2.a.d
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
