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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 203522.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
203522.p1 | 203522g2 | \([1, 1, 1, -5293692, -4817404195]\) | \(-128667913/4096\) | \(-522263189431352528896\) | \([]\) | \(13172544\) | \(2.7514\) | |
203522.p2 | 203522g1 | \([1, 1, 1, 303163, -24257573]\) | \(24167/16\) | \(-2040090583716220816\) | \([]\) | \(4390848\) | \(2.2021\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 203522.p have rank \(1\).
Complex multiplication
The elliptic curves in class 203522.p do not have complex multiplication.Modular form 203522.2.a.p
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.