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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 91035.z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
91035.z1 | 91035f2 | \([0, 0, 1, -32203848, 70341200734]\) | \(-209906535145406464/6559875\) | \(-115429448438584875\) | \([]\) | \(3649536\) | \(2.7778\) | |
91035.z2 | 91035f1 | \([0, 0, 1, -367608, 111649153]\) | \(-312217698304/125355195\) | \(-2205786088570476195\) | \([]\) | \(1216512\) | \(2.2285\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 91035.z have rank \(0\).
Complex multiplication
The elliptic curves in class 91035.z do not have complex multiplication.Modular form 91035.2.a.z
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.