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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 2370.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2370.m1 | 2370m2 | \([1, 0, 0, -4635130, -3841356970]\) | \(-11013097281880624350095521/830805227730\) | \(-830805227730\) | \([]\) | \(51000\) | \(2.1820\) | |
2370.m2 | 2370m1 | \([1, 0, 0, -3280, -517600]\) | \(-3902595313317121/113356365300000\) | \(-113356365300000\) | \([5]\) | \(10200\) | \(1.3773\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2370.m have rank \(0\).
Complex multiplication
The elliptic curves in class 2370.m do not have complex multiplication.Modular form 2370.2.a.m
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.