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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 301530d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
301530.d3 | 301530d1 | \([1, 1, 0, -30428, 1777152]\) | \(21047437081/2831760\) | \(419202109034640\) | \([2]\) | \(1351680\) | \(1.5332\) | \(\Gamma_0(N)\)-optimal |
301530.d2 | 301530d2 | \([1, 1, 0, -125648, -15381492]\) | \(1481933914201/171872100\) | \(25443239117796900\) | \([2, 2]\) | \(2703360\) | \(1.8798\) | |
301530.d4 | 301530d3 | \([1, 1, 0, 175882, -77556978]\) | \(4064592619079/19938671250\) | \(-2951638923972491250\) | \([2]\) | \(5406720\) | \(2.2263\) | |
301530.d1 | 301530d4 | \([1, 1, 0, -1950698, -1049454822]\) | \(5545326987531001/89921490\) | \(13311607712354610\) | \([2]\) | \(5406720\) | \(2.2263\) |
Rank
sage: E.rank()
The elliptic curves in class 301530d have rank \(0\).
Complex multiplication
The elliptic curves in class 301530d do not have complex multiplication.Modular form 301530.2.a.d
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.