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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 624i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 624.h4 | 624i1 | \([0, 1, 0, -312, -44460]\) | \(-822656953/207028224\) | \(-847987605504\) | \([2]\) | \(960\) | \(0.96808\) | \(\Gamma_0(N)\)-optimal |
| 624.h3 | 624i2 | \([0, 1, 0, -20792, -1150380]\) | \(242702053576633/2554695936\) | \(10464034553856\) | \([2, 2]\) | \(1920\) | \(1.3147\) | |
| 624.h1 | 624i3 | \([0, 1, 0, -331832, -73684908]\) | \(986551739719628473/111045168\) | \(454841008128\) | \([2]\) | \(3840\) | \(1.6612\) | |
| 624.h2 | 624i4 | \([0, 1, 0, -37432, 932948]\) | \(1416134368422073/725251155408\) | \(2970628732551168\) | \([4]\) | \(3840\) | \(1.6612\) |
Rank
sage: E.rank()
The elliptic curves in class 624i have rank \(0\).
Complex multiplication
The elliptic curves in class 624i do not have complex multiplication.Modular form 624.2.a.i
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.
