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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 77315.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
77315.f1 | 77315d1 | \([1, -1, 0, -11459, 135888]\) | \(15438249/8225\) | \(88659046081025\) | \([2]\) | \(194304\) | \(1.3677\) | \(\Gamma_0(N)\)-optimal |
77315.f2 | 77315d2 | \([1, -1, 0, 43766, 1030533]\) | \(860085351/541205\) | \(-5833765232131445\) | \([2]\) | \(388608\) | \(1.7142\) |
Rank
sage: E.rank()
The elliptic curves in class 77315.f have rank \(1\).
Complex multiplication
The elliptic curves in class 77315.f do not have complex multiplication.Modular form 77315.2.a.f
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.