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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 7938i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7938.b2 | 7938i1 | \([1, -1, 0, -194931, -33077339]\) | \(35801587017/16\) | \(366087922704\) | \([]\) | \(42336\) | \(1.5593\) | \(\Gamma_0(N)\)-optimal |
7938.b1 | 7938i2 | \([1, -1, 0, -230946, -19979884]\) | \(9074457/4096\) | \(614887132380401664\) | \([]\) | \(127008\) | \(2.1086\) |
Rank
sage: E.rank()
The elliptic curves in class 7938i have rank \(0\).
Complex multiplication
The elliptic curves in class 7938i do not have complex multiplication.Modular form 7938.2.a.i
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.