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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 57120.bd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
57120.bd1 | 57120o2 | \([0, -1, 0, -2360, -43308]\) | \(2840362499528/3186225\) | \(1631347200\) | \([2]\) | \(49152\) | \(0.68174\) | |
57120.bd2 | 57120o1 | \([0, -1, 0, -110, -1008]\) | \(-2320940224/6024375\) | \(-385560000\) | \([2]\) | \(24576\) | \(0.33517\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 57120.bd have rank \(1\).
Complex multiplication
The elliptic curves in class 57120.bd do not have complex multiplication.Modular form 57120.2.a.bd
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.