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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 7938t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7938.z2 | 7938t1 | \([1, -1, 1, -20, -17]\) | \(23625/8\) | \(285768\) | \([]\) | \(864\) | \(-0.25084\) | \(\Gamma_0(N)\)-optimal |
7938.z1 | 7938t2 | \([1, -1, 1, -650, 6535]\) | \(10481625/2\) | \(5786802\) | \([]\) | \(2592\) | \(0.29846\) |
Rank
sage: E.rank()
The elliptic curves in class 7938t have rank \(1\).
Complex multiplication
The elliptic curves in class 7938t do not have complex multiplication.Modular form 7938.2.a.t
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.