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SageMath
E = EllipticCurve("di1")
E.isogeny_class()
Elliptic curves in class 73008di
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 73008.di3 | 73008di1 | \([0, 0, 0, 3549, 57122]\) | \(9261/8\) | \(-4270451687424\) | \([]\) | \(103680\) | \(1.1111\) | \(\Gamma_0(N)\)-optimal |
| 73008.di2 | 73008di2 | \([0, 0, 0, -37011, -3633838]\) | \(-1167051/512\) | \(-2459780171956224\) | \([]\) | \(311040\) | \(1.6604\) | |
| 73008.di1 | 73008di3 | \([0, 0, 0, -77571, 8423298]\) | \(-132651/2\) | \(-778289820033024\) | \([]\) | \(311040\) | \(1.6604\) |
Rank
sage: E.rank()
The elliptic curves in class 73008di have rank \(1\).
Complex multiplication
The elliptic curves in class 73008di do not have complex multiplication.Modular form 73008.2.a.di
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.
\(\left(\begin{array}{rrr} 1 & 3 & 3 \\ 3 & 1 & 9 \\ 3 & 9 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
