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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 23400be
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
23400.w3 | 23400be1 | \([0, 0, 0, -1650, -14875]\) | \(2725888/1053\) | \(191909250000\) | \([2]\) | \(16384\) | \(0.86400\) | \(\Gamma_0(N)\)-optimal |
23400.w2 | 23400be2 | \([0, 0, 0, -11775, 481250]\) | \(61918288/1521\) | \(4435236000000\) | \([2, 2]\) | \(32768\) | \(1.2106\) | |
23400.w4 | 23400be3 | \([0, 0, 0, 1725, 1520750]\) | \(48668/85683\) | \(-999406512000000\) | \([2]\) | \(65536\) | \(1.5571\) | |
23400.w1 | 23400be4 | \([0, 0, 0, -187275, 31193750]\) | \(62275269892/39\) | \(454896000000\) | \([2]\) | \(65536\) | \(1.5571\) |
Rank
sage: E.rank()
The elliptic curves in class 23400be have rank \(1\).
Complex multiplication
The elliptic curves in class 23400be do not have complex multiplication.Modular form 23400.2.a.be
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 Cremona 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 Cremona labels.