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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 14400.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14400.k1 | 14400bs4 | \([0, 0, 0, -194700, 33046000]\) | \(546718898/405\) | \(604661760000000\) | \([2]\) | \(98304\) | \(1.7700\) | |
14400.k2 | 14400bs3 | \([0, 0, 0, -122700, -16346000]\) | \(136835858/1875\) | \(2799360000000000\) | \([2]\) | \(98304\) | \(1.7700\) | |
14400.k3 | 14400bs2 | \([0, 0, 0, -14700, 286000]\) | \(470596/225\) | \(167961600000000\) | \([2, 2]\) | \(49152\) | \(1.4234\) | |
14400.k4 | 14400bs1 | \([0, 0, 0, 3300, 34000]\) | \(21296/15\) | \(-2799360000000\) | \([2]\) | \(24576\) | \(1.0769\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 14400.k have rank \(2\).
Complex multiplication
The elliptic curves in class 14400.k do not have complex multiplication.Modular form 14400.2.a.k
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.