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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 22800.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
22800.t1 | 22800ca4 | \([0, -1, 0, -248408, 47667312]\) | \(26487576322129/44531250\) | \(2850000000000000\) | \([2]\) | \(147456\) | \(1.8608\) | |
22800.t2 | 22800ca2 | \([0, -1, 0, -20408, 243312]\) | \(14688124849/8122500\) | \(519840000000000\) | \([2, 2]\) | \(73728\) | \(1.5142\) | |
22800.t3 | 22800ca1 | \([0, -1, 0, -12408, -524688]\) | \(3301293169/22800\) | \(1459200000000\) | \([2]\) | \(36864\) | \(1.1676\) | \(\Gamma_0(N)\)-optimal |
22800.t4 | 22800ca3 | \([0, -1, 0, 79592, 1843312]\) | \(871257511151/527800050\) | \(-33779203200000000\) | \([2]\) | \(147456\) | \(1.8608\) |
Rank
sage: E.rank()
The elliptic curves in class 22800.t have rank \(1\).
Complex multiplication
The elliptic curves in class 22800.t do not have complex multiplication.Modular form 22800.2.a.t
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.