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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 357378l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
357378.l3 | 357378l1 | \([1, 0, 0, 168357063, -28208561031]\) | \(527737231583370421518916605167/305747584820092901684491776\) | \(-305747584820092901684491776\) | \([9]\) | \(217323648\) | \(3.7715\) | \(\Gamma_0(N)\)-optimal |
357378.l2 | 357378l2 | \([1, 0, 0, -2342114817, -46491207963039]\) | \(-1420850082701996138362832375655313/111479759347929068314392183576\) | \(-111479759347929068314392183576\) | \([3]\) | \(651970944\) | \(4.3208\) | |
357378.l1 | 357378l3 | \([1, 0, 0, -193149169647, -32672893402475361]\) | \(-796897103803836591798258764661693006193/325708012029457050422660406\) | \(-325708012029457050422660406\) | \([]\) | \(1955912832\) | \(4.8701\) |
Rank
sage: E.rank()
The elliptic curves in class 357378l have rank \(0\).
Complex multiplication
The elliptic curves in class 357378l do not have complex multiplication.Modular form 357378.2.a.l
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.