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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 377520.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
377520.o1 | 377520o2 | \([0, -1, 0, -26781, -1917375]\) | \(-4684079104/823875\) | \(-373643473632000\) | \([]\) | \(1166400\) | \(1.5219\) | |
377520.o2 | 377520o1 | \([0, -1, 0, 2259, 10881]\) | \(2809856/1755\) | \(-795926926080\) | \([]\) | \(388800\) | \(0.97264\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 377520.o have rank \(1\).
Complex multiplication
The elliptic curves in class 377520.o do not have complex multiplication.Modular form 377520.2.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 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.