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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 2394.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2394.d1 | 2394a4 | \([1, -1, 0, -11922, 364940]\) | \(9521387989875/2634569336\) | \(51856228240488\) | \([2]\) | \(6912\) | \(1.3390\) | |
2394.d2 | 2394a2 | \([1, -1, 0, -10977, 445419]\) | \(5417927574172875/247646\) | \(6686442\) | \([6]\) | \(2304\) | \(0.78973\) | |
2394.d3 | 2394a3 | \([1, -1, 0, -4362, -105292]\) | \(466385893875/21509824\) | \(423377865792\) | \([2]\) | \(3456\) | \(0.99246\) | |
2394.d4 | 2394a1 | \([1, -1, 0, -687, 7065]\) | \(1329185824875/8941324\) | \(241415748\) | \([6]\) | \(1152\) | \(0.44316\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2394.d have rank \(1\).
Complex multiplication
The elliptic curves in class 2394.d do not have complex multiplication.Modular form 2394.2.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.
\(\left(\begin{array}{rrrr} 1 & 3 & 2 & 6 \\ 3 & 1 & 6 & 2 \\ 2 & 6 & 1 & 3 \\ 6 & 2 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.