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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 374790r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
374790.r4 | 374790r1 | \([1, 1, 0, -949968, 252868608]\) | \(106827039259849/30599112960\) | \(27156825387334805760\) | \([2]\) | \(11796480\) | \(2.4355\) | \(\Gamma_0(N)\)-optimal |
374790.r2 | 374790r2 | \([1, 1, 0, -13942688, 20030386992]\) | \(337748263783145929/47358464400\) | \(42030811481507456400\) | \([2, 2]\) | \(23592960\) | \(2.7821\) | |
374790.r1 | 374790r3 | \([1, 1, 0, -223075508, 1282314261948]\) | \(1383277217333832812809/27202500\) | \(24142318882402500\) | \([2]\) | \(47185920\) | \(3.1287\) | |
374790.r3 | 374790r4 | \([1, 1, 0, -12693388, 23767543012]\) | \(-254850956966062729/127607200177860\) | \(-113251859879954604702660\) | \([2]\) | \(47185920\) | \(3.1287\) |
Rank
sage: E.rank()
The elliptic curves in class 374790r have rank \(1\).
Complex multiplication
The elliptic curves in class 374790r do not have complex multiplication.Modular form 374790.2.a.r
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.