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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 59248.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
59248.s1 | 59248w2 | \([0, 0, 0, -3954275, -2999335838]\) | \(926859375/9604\) | \(70853714578188910592\) | \([2]\) | \(1271808\) | \(2.6260\) | |
59248.s2 | 59248w1 | \([0, 0, 0, -60835, -115854174]\) | \(-3375/784\) | \(-5783976700260319232\) | \([2]\) | \(635904\) | \(2.2794\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 59248.s have rank \(2\).
Complex multiplication
The elliptic curves in class 59248.s do not have complex multiplication.Modular form 59248.2.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.