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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 377520.bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 377520.bd1 | 377520bd4 | \([0, -1, 0, -2315496, -1286386704]\) | \(189208196468929/10860320250\) | \(78805892310672384000\) | \([2]\) | \(9953280\) | \(2.5719\) | |
| 377520.bd2 | 377520bd2 | \([0, -1, 0, -398856, 96660720]\) | \(967068262369/4928040\) | \(35759404934922240\) | \([2]\) | \(3317760\) | \(2.0226\) | |
| 377520.bd3 | 377520bd1 | \([0, -1, 0, -11656, 3113200]\) | \(-24137569/561600\) | \(-4075145861529600\) | \([2]\) | \(1658880\) | \(1.6760\) | \(\Gamma_0(N)\)-optimal |
| 377520.bd4 | 377520bd3 | \([0, -1, 0, 104504, -82194704]\) | \(17394111071/411937500\) | \(-2989147789056000000\) | \([2]\) | \(4976640\) | \(2.2253\) |
Rank
sage: E.rank()
The elliptic curves in class 377520.bd have rank \(1\).
Complex multiplication
The elliptic curves in class 377520.bd do not have complex multiplication.Modular form 377520.2.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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
