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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 74704g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
74704.j2 | 74704g1 | \([0, 0, 0, -825299, -288581998]\) | \(-15177411906818559273/167619938752\) | \(-686571269128192\) | \([2]\) | \(663552\) | \(2.0007\) | \(\Gamma_0(N)\)-optimal |
74704.j1 | 74704g2 | \([0, 0, 0, -13204819, -18469145070]\) | \(62167173500157644301993/7582456\) | \(31057739776\) | \([2]\) | \(1327104\) | \(2.3473\) |
Rank
sage: E.rank()
The elliptic curves in class 74704g have rank \(0\).
Complex multiplication
The elliptic curves in class 74704g do not have complex multiplication.Modular form 74704.2.a.g
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 Cremona 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 Cremona labels.