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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 9240d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9240.i4 | 9240d1 | \([0, -1, 0, 100, -780]\) | \(427694384/1188495\) | \(-304254720\) | \([2]\) | \(3072\) | \(0.31133\) | \(\Gamma_0(N)\)-optimal |
| 9240.i3 | 9240d2 | \([0, -1, 0, -880, -8228]\) | \(73682642884/12006225\) | \(12294374400\) | \([2, 2]\) | \(6144\) | \(0.65790\) | |
| 9240.i1 | 9240d3 | \([0, -1, 0, -13480, -597908]\) | \(132280446972242/4611915\) | \(9445201920\) | \([2]\) | \(12288\) | \(1.0045\) | |
| 9240.i2 | 9240d4 | \([0, -1, 0, -3960, 89100]\) | \(3354200221682/315748125\) | \(646652160000\) | \([2]\) | \(12288\) | \(1.0045\) |
Rank
sage: E.rank()
The elliptic curves in class 9240d have rank \(0\).
Complex multiplication
The elliptic curves in class 9240d do not have complex multiplication.Modular form 9240.2.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 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.
