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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 385320i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 385320.i4 | 385320i1 | \([0, -1, 0, 3324, 127620]\) | \(3286064/7695\) | \(-9508427585280\) | \([2]\) | \(884736\) | \(1.1743\) | \(\Gamma_0(N)\)-optimal |
| 385320.i3 | 385320i2 | \([0, -1, 0, -27096, 1429596]\) | \(445138564/81225\) | \(401466942489600\) | \([2, 2]\) | \(1769472\) | \(1.5208\) | |
| 385320.i1 | 385320i3 | \([0, -1, 0, -412416, 102075180]\) | \(784767874322/35625\) | \(352163984640000\) | \([2]\) | \(3538944\) | \(1.8674\) | |
| 385320.i2 | 385320i4 | \([0, -1, 0, -128496, -16376244]\) | \(23735908082/1954815\) | \(19323942165166080\) | \([2]\) | \(3538944\) | \(1.8674\) |
Rank
sage: E.rank()
The elliptic curves in class 385320i have rank \(1\).
Complex multiplication
The elliptic curves in class 385320i do not have complex multiplication.Modular form 385320.2.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.
