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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 346800m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 346800.m1 | 346800m1 | \([0, -1, 0, -2353423, -1388698358]\) | \(29860725364736/3581577\) | \(172901123932626000\) | \([2]\) | \(8626176\) | \(2.3324\) | \(\Gamma_0(N)\)-optimal |
| 346800.m2 | 346800m2 | \([0, -1, 0, -2158348, -1628640608]\) | \(-1439609866256/651714363\) | \(-503385612966513504000\) | \([2]\) | \(17252352\) | \(2.6790\) |
Rank
sage: E.rank()
The elliptic curves in class 346800m have rank \(0\).
Complex multiplication
The elliptic curves in class 346800m do not have complex multiplication.Modular form 346800.2.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 Cremona 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 Cremona labels.
