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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 370300o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 370300.o1 | 370300o1 | \([0, -1, 0, -34818916658, -2500742527665563]\) | \(-126142795384287538429696/9315359375\) | \(-344751876608152343750000\) | \([]\) | \(448892928\) | \(4.4127\) | \(\Gamma_0(N)\)-optimal |
| 370300.o2 | 370300o2 | \([0, -1, 0, -34468454158, -2553548134228063]\) | \(-122372013839654770813696/5297595236711512175\) | \(-196058555107188535340112143750000\) | \([]\) | \(1346678784\) | \(4.9620\) |
Rank
sage: E.rank()
The elliptic curves in class 370300o have rank \(0\).
Complex multiplication
The elliptic curves in class 370300o do not have complex multiplication.Modular form 370300.2.a.o
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.
