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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 24048.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
24048.c1 | 24048i2 | \([0, 0, 0, -17931, -921670]\) | \(213525509833/669336\) | \(1998626586624\) | \([2]\) | \(55296\) | \(1.2276\) | |
24048.c2 | 24048i1 | \([0, 0, 0, -651, -26566]\) | \(-10218313/96192\) | \(-287227772928\) | \([2]\) | \(27648\) | \(0.88103\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 24048.c have rank \(0\).
Complex multiplication
The elliptic curves in class 24048.c do not have complex multiplication.Modular form 24048.2.a.c
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.