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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 71148.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
71148.c1 | 71148bg2 | \([0, -1, 0, -2160132, 1222712856]\) | \(-2527934627152/9\) | \(-3968637716736\) | \([]\) | \(1088640\) | \(2.0593\) | |
71148.c2 | 71148bg1 | \([0, -1, 0, -25692, 1813176]\) | \(-4253392/729\) | \(-321459655055616\) | \([]\) | \(362880\) | \(1.5100\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 71148.c have rank \(2\).
Complex multiplication
The elliptic curves in class 71148.c do not have complex multiplication.Modular form 71148.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.