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SageMath
E = EllipticCurve("di1")
E.isogeny_class()
Elliptic curves in class 242760di
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 242760.di3 | 242760di1 | \([0, 1, 0, -91420, -10669120]\) | \(13674725584/945\) | \(5839360692480\) | \([2]\) | \(884736\) | \(1.5034\) | \(\Gamma_0(N)\)-optimal |
| 242760.di2 | 242760di2 | \([0, 1, 0, -97200, -9249552]\) | \(4108974916/893025\) | \(22072783417574400\) | \([2, 2]\) | \(1769472\) | \(1.8499\) | |
| 242760.di1 | 242760di3 | \([0, 1, 0, -501800, 128638128]\) | \(282678688658/18600435\) | \(919489092080670720\) | \([2]\) | \(3538944\) | \(2.1965\) | |
| 242760.di4 | 242760di4 | \([0, 1, 0, 214920, -56192400]\) | \(22208984782/40516875\) | \(-2002900717520640000\) | \([2]\) | \(3538944\) | \(2.1965\) |
Rank
sage: E.rank()
The elliptic curves in class 242760di have rank \(0\).
Complex multiplication
The elliptic curves in class 242760di do not have complex multiplication.Modular form 242760.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
