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SageMath
E = EllipticCurve("cr1")
E.isogeny_class()
Elliptic curves in class 101400.cr
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 101400.cr1 | 101400bb4 | \([0, 1, 0, -24574008, 46865149488]\) | \(10625310339698/3855735\) | \(595548684787680000000\) | \([2]\) | \(6193152\) | \(2.9548\) | |
| 101400.cr2 | 101400bb3 | \([0, 1, 0, -12744008, -17158810512]\) | \(1481943889298/34543665\) | \(5335541539679520000000\) | \([2]\) | \(6193152\) | \(2.9548\) | |
| 101400.cr3 | 101400bb2 | \([0, 1, 0, -1759008, 505069488]\) | \(7793764996/3080025\) | \(237867078243600000000\) | \([2, 2]\) | \(3096576\) | \(2.6083\) | |
| 101400.cr4 | 101400bb1 | \([0, 1, 0, 353492, 57219488]\) | \(253012016/219375\) | \(-4235524897500000000\) | \([2]\) | \(1548288\) | \(2.2617\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 101400.cr have rank \(0\).
Complex multiplication
The elliptic curves in class 101400.cr do not have complex multiplication.Modular form 101400.2.a.cr
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
