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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 265200.i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 265200.i1 | 265200i3 | \([0, -1, 0, -418408, 104299312]\) | \(126574061279329/16286595\) | \(1042342080000000\) | \([2]\) | \(2752512\) | \(1.9028\) | |
| 265200.i2 | 265200i2 | \([0, -1, 0, -28408, 1339312]\) | \(39616946929/10989225\) | \(703310400000000\) | \([2, 2]\) | \(1376256\) | \(1.5562\) | |
| 265200.i3 | 265200i1 | \([0, -1, 0, -10408, -388688]\) | \(1948441249/89505\) | \(5728320000000\) | \([2]\) | \(688128\) | \(1.2097\) | \(\Gamma_0(N)\)-optimal |
| 265200.i4 | 265200i4 | \([0, -1, 0, 73592, 8683312]\) | \(688699320191/910381875\) | \(-58264440000000000\) | \([2]\) | \(2752512\) | \(1.9028\) |
Rank
sage: E.rank()
The elliptic curves in class 265200.i have rank \(1\).
Complex multiplication
The elliptic curves in class 265200.i do not have complex multiplication.Modular form 265200.2.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 LMFDB 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 LMFDB labels.
