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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 179088.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
179088.b1 | 179088z2 | \([0, -1, 0, -43515203152, 3493907794853824]\) | \(-2224778660867235879101476628566993/16157901081011429376\) | \(-66182762827822814724096\) | \([]\) | \(225628416\) | \(4.4315\) | |
179088.b2 | 179088z1 | \([0, -1, 0, -534728272, 4839647313856]\) | \(-4128223528775369483123266513/81108488685750967074816\) | \(-332220369656835961138446336\) | \([]\) | \(75209472\) | \(3.8822\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 179088.b have rank \(1\).
Complex multiplication
The elliptic curves in class 179088.b do not have complex multiplication.Modular form 179088.2.a.b
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.