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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 13950.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
13950.d1 | 13950r3 | \([1, -1, 0, -340542, 73280866]\) | \(383432500775449/18701300250\) | \(213019498160156250\) | \([2]\) | \(221184\) | \(2.0846\) | |
13950.d2 | 13950r2 | \([1, -1, 0, -59292, -4062884]\) | \(2023804595449/540562500\) | \(6157344726562500\) | \([2, 2]\) | \(110592\) | \(1.7380\) | |
13950.d3 | 13950r1 | \([1, -1, 0, -54792, -4922384]\) | \(1597099875769/186000\) | \(2118656250000\) | \([2]\) | \(55296\) | \(1.3915\) | \(\Gamma_0(N)\)-optimal |
13950.d4 | 13950r4 | \([1, -1, 0, 149958, -26452634]\) | \(32740359775271/45410156250\) | \(-517250061035156250\) | \([2]\) | \(221184\) | \(2.0846\) |
Rank
sage: E.rank()
The elliptic curves in class 13950.d have rank \(0\).
Complex multiplication
The elliptic curves in class 13950.d do not have complex multiplication.Modular form 13950.2.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 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.