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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 7938.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7938.m1 | 7938b2 | \([1, -1, 0, -4713, 59597]\) | \(9074457/4096\) | \(5226454388736\) | \([]\) | \(18144\) | \(1.1356\) | |
7938.m2 | 7938b1 | \([1, -1, 0, -3978, 97572]\) | \(35801587017/16\) | \(3111696\) | \([3]\) | \(6048\) | \(0.58631\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7938.m have rank \(1\).
Complex multiplication
The elliptic curves in class 7938.m do not have complex multiplication.Modular form 7938.2.a.m
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.