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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 154560.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
154560.c1 | 154560hs4 | \([0, -1, 0, -53843284321, -4808878531214879]\) | \(65853432878493908038433301506521/38511703125000000\) | \(10095611904000000000000\) | \([2]\) | \(247726080\) | \(4.4474\) | |
154560.c2 | 154560hs2 | \([0, -1, 0, -3365224801, -75136969936415]\) | \(16077778198622525072705635801/388799208512064000000\) | \(101921379716186505216000000\) | \([2, 2]\) | \(123863040\) | \(4.1009\) | |
154560.c3 | 154560hs3 | \([0, -1, 0, -3239784801, -80996849360415]\) | \(-14346048055032350809895395801/2509530875136386550792000\) | \(-657858461731752915970818048000\) | \([2]\) | \(247726080\) | \(4.4474\) | |
154560.c4 | 154560hs1 | \([0, -1, 0, -218186081, -1081484185119]\) | \(4381924769947287308715481/608122186185572352000\) | \(159415582375430678642688000\) | \([2]\) | \(61931520\) | \(3.7543\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 154560.c have rank \(0\).
Complex multiplication
The elliptic curves in class 154560.c do not have complex multiplication.Modular form 154560.2.a.c
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.