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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 59248f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
59248.e2 | 59248f1 | \([0, 1, 0, -14988, 902572]\) | \(-9826000/3703\) | \(-140333285623552\) | \([2]\) | \(168960\) | \(1.4244\) | \(\Gamma_0(N)\)-optimal |
59248.e1 | 59248f2 | \([0, 1, 0, -258328, 50446596]\) | \(12576878500/1127\) | \(170840521628672\) | \([2]\) | \(337920\) | \(1.7710\) |
Rank
sage: E.rank()
The elliptic curves in class 59248f have rank \(0\).
Complex multiplication
The elliptic curves in class 59248f do not have complex multiplication.Modular form 59248.2.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 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.