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SageMath
E = EllipticCurve("dg1")
E.isogeny_class()
Elliptic curves in class 77760.dg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
77760.dg1 | 77760er1 | \([0, 0, 0, -9612, -362736]\) | \(-171307467/10\) | \(-5733089280\) | \([]\) | \(62208\) | \(0.93516\) | \(\Gamma_0(N)\)-optimal |
77760.dg2 | 77760er2 | \([0, 0, 0, -972, -983664]\) | \(-243/1000\) | \(-417942208512000\) | \([]\) | \(186624\) | \(1.4845\) |
Rank
sage: E.rank()
The elliptic curves in class 77760.dg have rank \(0\).
Complex multiplication
The elliptic curves in class 77760.dg do not have complex multiplication.Modular form 77760.2.a.dg
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.