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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 159120.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
159120.s1 | 159120dv2 | \([0, 0, 0, -14223, 629822]\) | \(1705021456336/68471325\) | \(12778392556800\) | \([2]\) | \(393216\) | \(1.2812\) | |
159120.s2 | 159120dv1 | \([0, 0, 0, 402, 36047]\) | \(615962624/48481875\) | \(-565492590000\) | \([2]\) | \(196608\) | \(0.93460\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 159120.s have rank \(2\).
Complex multiplication
The elliptic curves in class 159120.s do not have complex multiplication.Modular form 159120.2.a.s
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.