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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 37485.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
37485.q1 | 37485n1 | \([1, -1, 1, -13164962, 18388878736]\) | \(231598843578097029/614125\) | \(669118290269625\) | \([2]\) | \(1290240\) | \(2.5056\) | \(\Gamma_0(N)\)-optimal |
37485.q2 | 37485n2 | \([1, -1, 1, -13159817, 18403965934]\) | \(-231327416180313909/377149515625\) | \(-410922270011833453125\) | \([2]\) | \(2580480\) | \(2.8522\) |
Rank
sage: E.rank()
The elliptic curves in class 37485.q have rank \(1\).
Complex multiplication
The elliptic curves in class 37485.q do not have complex multiplication.Modular form 37485.2.a.q
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.